Question 1

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set.
-$$x ^ { 2 } + y ^ { 2 } + 4 x + 8 y + 11 = 0$$
A) $( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$; Center: $( - 2 , - 4 )$; Radius: 3
B) $( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 0 ;$ Degenerate case (single point $) : \{ ( - 2 , - 4 ) \}$
C) $( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$; Center: $( 2,4 )$; Radius: 3
D) $( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = - 9$; Degenerate case: \{ \}

Accepted Answer

To rewrite the given equation in standard form, complete the square for both $x$ and $y$ terms: $x^2 + 4x + 4 + y^2 + 8y + 16 = 0 + 4 + 16$, which simplifies to $(x + 2)^2 + (y + 4)^2 = 20 - 11 = 9$. The center is at $(-2, -4)$ and the radius is $\sqrt{9} = 3$.

Question 2

Solve the problem.
-A cell tower is a site where antennas, transmitters, and receivers are placed to create a cellular network. Suppose that a cell tower is located at a point A(-7, -6) on a map and its range is 2.5 mi. Write an equation that represents the boundary of the area that can receive a signal from the tower.
Assume that all distances are in miles. 
A) $( x + 7 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 6.25$
B) $( x + 7 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 2.5$
C) $| x + 7 | + | ( y + 6 ) | = 2.5$
D) $| x - 7 | + | ( y - 6 ) | = 2.5$

Accepted Answer

The equation represents a circle with center at (-7, -6) and radius 2.5. The equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where (h, k) is the center and r is the radius. Substituting h = -7, k = -6, and r = 2.5, we get $(x + 7)^2 + (y + 6)^2 = 6.25$, since $2.5^2 = 6.25$.

Question 3

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set.
-$$x ^ { 2 } + y ^ { 2 } - 4 x + 2 y + 5 = 0$$
A) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$; Center: $( - 2,1 )$; Radius: 5
B) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$; Center: $( 2 , - 1 )$; Radius: 5
C) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 0$; Degenerate case (single point): $\{ ( 2 , - 1 ) \}$
D) $( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = - 5$; Degenerate case: \{ \}

Accepted Answer

The answer of Write the equation in standard form: \((...

Question 4

Solve the problem.
-Find the shortest distance from the origin to a point on the circle defined by $$x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$$
A) $2 \sqrt { 130 } - + 3$
B) $\sqrt { 130 } + 3$
C) $\sqrt { 130 } - 3$
D) $2 \sqrt { 130 } - 3$

Accepted Answer

The given equation can be rewritten in the form $(x - 7)^2 + (y - 9)^2 = 25$, which represents a circle with center (7, 9) and radius 5. The shortest distance from the origin (0, 0) to the circle is the distance from the origin to the center minus the radius: $\sqrt{7^2 + 9^2} - 5 = \sqrt{130} - 5$.

Question 5

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$$

A) $( x + 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 16$
Center: $( 4 , - 5 ) ; r = 4$

B) $( x + 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 16$
Center: $( - 4,5 ) ; r = 4$

C) $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$
Center: $( 8 , - 10 ) ; r = 25$

D) $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$
Center: $( - 8,10 ) ; r = 25$

Accepted Answer

To rewrite the equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$, complete the square for both $x$ and $y$. The given equation is $x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$. Group $x$ and $y$ terms: $(x^2 + 8x) + (y^2 - 10y) = -25$. To complete the square, add and subtract $(\frac{8}{2})^2 = 16$ for $x$ and add and subtract $(\frac{10}{2})^2 = 25$ for $y$, then rearrange: $(x^2 + 8x + 16) + (y^2 - 10y + 25) = -25 + 16 + 25$. This simplifies to $(x + 4)^2 + (y - 5)^2 = 16$, which matches choice B. The center is at $(-4, 5)$ and the radius $r = \sqrt{16} = 4$.

Question 6

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph.
-$$x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$$
A) $( x - 3 ) ^ { 2 } + y ^ { 2 } = 7$

B) $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

C) $( x - 3 ) ^ { 2 } + y ^ { 2 } = 7$

D) $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

Accepted Answer

The answer of Write the equation in standard form to...

Question 7

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-Explain what it means for a relation to define y as a function of x.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$$
A) $( x + 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

B) $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( - 3,3 ) ; r = 10$

C) $( x + 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

D) $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

Accepted Answer

To rewrite the equation in the form $(x - h)^2 + (y - k)^2 = r^2$, we complete the square for both $x$ and $y$. The given equation is $x^2 + y^2 - 6x + 6y - 82 = 0$. For $x$, we add and subtract $(\frac{6}{2})^2 = 9$, and for $y$, we add and subtract $(\frac{6}{2})^2 = 9$, resulting in $x^2 - 6x + 9 + y^2 + 6y + 9 = 82 + 9 + 9$, which simplifies to $(x - 3)^2 + (y + 3)^2 = 100$. The center is $(3, -3)$ and the radius $r = \sqrt{100} = 10$.

Question 9

Write the equation in standard form to find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } + 6 x + 14 y + 37 = 0$$
A) $( x + 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 21 ;$ center $( - 3 , - 7 )$, radius $\sqrt { 21 }$
B) $( x + 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 21 ;$ center $( - 3 , - 7 )$, radius 21
C) $( x + 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 21 ;$ center $( 3,7 )$, radius 21
D) $( x - 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 21 ;$ center $( 3,7 )$, radius $\sqrt { 21 }$

Accepted Answer

To convert the given equation to the standard form of a circle $(x - h)^2 + (y - k)^2 = r^2$, we complete the square for both $x$ and $y$ terms. For $x^2 + 6x$, we add and subtract $(\frac{6}{2})^2 = 9$, and for $y^2 + 14y$, we add and subtract $(\frac{14}{2})^2 = 49$. The equation becomes $x^2 + 6x + 9 + y^2 + 14y + 49 = 0 + 9 + 49$, simplifying to $(x + 3)^2 + (y + 7)^2 = 58 - 37 = 21$. The center is at $(-3, -7)$ and the radius is $\sqrt{21}$.

Question 10

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-A set of ordered pairs (x, y) is called a ________in x and y. The set of x values in the relation is called the________ of the relation. The set of ________values is called the range of the
relation.

Accepted Answer

The answer of Write the word or phrase that best...

Question 11

Write the given equation in the form $$( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$$ . Identify the center and radius.
-$$25 x ^ { 2 } + 25 y ^ { 2 } - 20 x + 60 y - 360 = 0$$
A) Center: $\left( - \frac { 4 } { 5 } , \frac { 12 } { 5 } \right) ; r = 360$
B) Center: $\left( - \frac { 2 } { 5 } , \frac { 6 } { 5 } \right) ; r = 4$
C) Center: $\left( \frac { 2 } { 5 } , - \frac { 6 } { 5 } \right) ; r = 4$
D) Center: $\left( \frac { 4 } { 5 } , - \frac { 12 } { 5 } \right) ; r = 360$

Accepted Answer

The answer of Write the given equation in the form...

Question 12

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$$
A) $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( - 22,0 ) ; r = 21$

B) $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( 0,22 ) ; r = 21$

C) $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( - 11,0 ) ; r = 10$

D) $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( 0,11 ) ; r = 10$

Accepted Answer

To write the equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$, complete the square for the x-terms. The given equation is $x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$. Completing the square for the x-term involves adding and subtracting $(\frac{22}{2})^2 = 121$, leading to $x ^ { 2 } + 22 x + 121 + y ^ { 2 } = -21 + 121$, which simplifies to $(x + 11)^2 + y^2 = 100$. The center is $(-11, 0)$ and the radius $r = \sqrt{100} = 10$.

Question 13

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-Given a function defined by y = f (x), the statement f (2) = 4 is equivalent to what ordered pair?

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-If the graph of a set of points (x, y) has two points aligned vertically then the relation (does/does not)
define y as a function of x.

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-Given a function defined by y= f (x), to find the x-intercept(s), substitute 0 for ________and solve for x.

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Write the given equation in the form $$( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0$$
A) Center: $( 0 , - 4 ) ; r = 5$
B) Center: $( 0,8 ) ; r = 11$
C) Center: $( 0,4 ) ; r = \sqrt { 5 }$
D) Center: $( 0 , - 8 ) ; r = 11$

Accepted Answer

The answer of Write the given equation in the form...

Question 17

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-Given a function defined by y = f (x), to find the -intercept, evaluate f (0).

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Identify the center and radius of the circle.
-$$x ^ { 2 } - 10 x + y ^ { 2 } = 11$$
A) Center: $( 10,0 ) ; \quad r = 36$
B) Center: $( 0 , - 5 ) ; \quad r = 6$
C) Center: $( 5,0 ) ; \quad r = 6$
D) Center: $( 10,0 ) ; \quad r = \sqrt { 11 }$

Accepted Answer

To find the center and radius of the circle given by the equation $x^2 - 10x + y^2 = 11$, we complete the square for the x-terms. The equation can be rewritten as $(x^2 - 10x + 25) + y^2 = 11 + 25$ to complete the square, resulting in $(x - 5)^2 + y^2 = 36$. This shows the circle has a center at $(5, 0)$ and a radius $r = \sqrt{36} = 6$.

Question 19

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$$
A) $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( 16,8 ) ; r = 20$

B) $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( - 16 , - 8 ) ; r = 20$

C) $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( - 8 , - 4 ) ; r = 10$

D) $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( 8,4 ) ; r = 10$

Accepted Answer

To get the equation in the form $(x - h)^2 + (y - k)^2 = r^2$, complete the square for both $x$ and $y$. The given equation is $x^2 + y^2 + 16x + 8y - 20 = 0$. Completing the square:- For $x^2 + 16x$, add and subtract $(\frac{16}{2})^2 = 64$.- For $y^2 + 8y$, add and subtract $(\frac{8}{2})^2 = 16$.So, the equation becomes $x^2 + 16x + 64 + y^2 + 8y + 16 - 20 - 64 - 16 = 0$, which simplifies to $(x + 8)^2 + (y + 4)^2 = 100$. The center is at $(-8, -4)$ and the radius $r = \sqrt{100} = 10$.

Question 20

Determine the solution set for the equation.
-$$( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 0$$
A) $\{ ( 4 , - 2 ) \}$
B) $\{ ( - 4,2 ) \}$
C) \{ \}
D) $\{ ( 16,4 ) \}$

Accepted Answer

The equation represents a circle with radius 0, centered at (-4, 2). The only point on this "circle" is its center.

Quiz 2: Functions and Relations

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set. - $x ^ { 2 } + y ^ { 2 } + 4 x + 8 y + 11 = 0$

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set. - $x ^ { 2 } + y ^ { 2 } - 4 x + 2 y + 5 = 0$

Solve the problem. -Find the shortest distance from the origin to a point on the circle defined by $x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. - $x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Explain what it means for a relation to define y as a function of x.

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$

Write the equation in standard form to find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 6 x + 14 y + 37 = 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A set of ordered pairs (x, y) is called a in x and y. The set of x values in the relation is called the of the relation. The set of values is called the range of the relation.

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $25 x ^ { 2 } + 25 y ^ { 2 } - 20 x + 60 y - 360 = 0$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), the statement f (2) = 4 is equivalent to what ordered pair?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the graph of a set of points (x, y) has two points aligned vertically then the relation (does/does not) define y as a function of x.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y= f (x), to find the x-intercept(s), substitute 0 for ________and solve for x.

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), to find the -intercept, evaluate f (0).

Identify the center and radius of the circle. - $x ^ { 2 } - 10 x + y ^ { 2 } = 11$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$

Determine the solution set for the equation. - $( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 0$

Quiz 2: Functions and Relations

Solve the problem. -Find the shortest distance from the origin to a point on the circle defined by x2+y2−14x−18y+121=0. x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }x2+y2−14x−18y+121=0.

Write the given equation in the form (x−h) 2+(y−k) 2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h) 2+(y−k) 2=r2 . Identify the center and radius. - x2+y2+8x−10y+25=0x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0x2+y2+8x−10y+25=0

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. - x2+y2−6x+5=0x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0x2+y2−6x+5=0

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Explain what it means for a relation to define y as a function of x.

Write the given equation in the form (x−h) 2+(y−k) 2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h) 2+(y−k) 2=r2 . Identify the center and radius. - x2+y2−6x+6y−82=0x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0x2+y2−6x+6y−82=0

Write the equation in standard form to find the center and radius of the circle. - x2+y2+6x+14y+37=0x ^ { 2 } + y ^ { 2 } + 6 x + 14 y + 37 = 0x2+y2+6x+14y+37=0

Write the given equation in the form (x−h) 2+(y−k) 2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h) 2+(y−k) 2=r2 . Identify the center and radius. - 25x2+25y2−20x+60y−360=025 x ^ { 2 } + 25 y ^ { 2 } - 20 x + 60 y - 360 = 025x2+25y2−20x+60y−360=0

Write the given equation in the form (x−h) 2+(y−k) 2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h) 2+(y−k) 2=r2 . Identify the center and radius. - x2+y2+22x+21=0x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0x2+y2+22x+21=0

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), the statement f (2) = 4 is equivalent to what ordered pair?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the graph of a set of points (x, y) has two points aligned vertically then the relation (does/does not) define y as a function of x.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y= f (x), to find the x-intercept(s), substitute 0 for ________and solve for x.

Write the given equation in the form (x−h) 2+(y−k) 2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h) 2+(y−k) 2=r2 . Identify the center and radius. - x2+y2−8y+11=0x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0x2+y2−8y+11=0

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), to find the -intercept, evaluate f (0).

Identify the center and radius of the circle. - x2−10x+y2=11x ^ { 2 } - 10 x + y ^ { 2 } = 11x2−10x+y2=11

Write the given equation in the form (x−h) 2+(y−k) 2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h) 2+(y−k) 2=r2 . Identify the center and radius. - x2+y2+16x+8y−20=0x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0x2+y2+16x+8y−20=0

Determine the solution set for the equation. - (x+4) 2+(y−2) 2=0( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 0(x+4) 2+(y−2) 2=0

Solve the problem. -Find the shortest distance from the origin to a point on the circle defined by $x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. - $x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$

Write the equation in standard form to find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 6 x + 14 y + 37 = 0$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $25 x ^ { 2 } + 25 y ^ { 2 } - 20 x + 60 y - 360 = 0$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0$

Identify the center and radius of the circle. - $x ^ { 2 } - 10 x + y ^ { 2 } = 11$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$

Determine the solution set for the equation. - $( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 0$