Question 1

Graph the circle.
-$x^{2}+(y-3)^{2}=16$

A)  
B)  
C) 
D)

Accepted Answer

The answer of Graph the circle.
-$x^{2}+(y-3)^{2}=16$

A)  
B)  
C)...

Question 2

Graph the circle.
-$(x-5)^{2}+y^{2}=9$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the circle.
-$(x-5)^{2}+y^{2}=9$

A)

B)

C)

D) ...

Question 3

Graph the circle.
-$x^{2}+y^{2}-8 x-8 y+7=0$

A)

B)  
C)

D)

Accepted Answer

The answer of Graph the circle.
-$x^{2}+y^{2}-8 x-8 y+7=0$

A)

B) ...

Question 4

Graph the circle.
-$x^{2}+y^{2}+2 x+8 y+8=0$

A) 
B)  
C) 
D)

Accepted Answer

The answer of Graph the circle.
-$x^{2}+y^{2}+2 x+8 y+8=0$

A) 
B) ...

Question 5

Graph the circle.
-$2 y^{2}=32-2 x^{2}$

A) 
B)  
C)  
D)

Accepted Answer

The answer of Graph the circle.
-$2 y^{2}=32-2 x^{2}$

A) 
B) ...

Question 6

Graph the ellipse.
-$\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$

A) 
B) 
C)  
D)

Accepted Answer

The answer of Graph the ellipse.
-$\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$

A) 
B) 
C)  
D)...

Question 7

Graph the ellipse.
-$\frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the ellipse.
-$\frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

A) 
B) 
C) 
D) ...

Question 8

Graph the ellipse.
-$\frac{(x+1)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

A)  
B)  
C)  
D)

Accepted Answer

The answer of Graph the ellipse.
-$\frac{(x+1)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

A)  
B)  
C)...

Question 9

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given?
-$x^{2}+y^{2}=25$

A) $y_{1}=\sqrt{25-x^{2}}, y_2=\sqrt{25+x^{2}}$

B) $\mathrm{y}_{1}=\sqrt{25-\mathrm{x}^{2}}, \mathrm{y}_2=-\sqrt{25-\mathrm{x}^{2}}$

C) $y_{1}=\sqrt{x^{2}-25}, y_{2}=-\sqrt{x^{2}-25}$

D) $y_{1}=\sqrt{25+x^{2}}, y_{2}=-\sqrt{25-x^{2}}$

Accepted Answer

The answer of The circle or ellipse shown in the...

Question 10

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given?
-$\frac{x^{2}}{25}+\frac{y^{2}}{25}=1$

A) $y_{1}=\sqrt{25-x^{2}}, y_2=-\sqrt{25-x^{2}}$

B) $y_{1}=\sqrt{25+x^{2}}, y_{2}=-\sqrt{25+x^{2}}$

C) $y_{1}=\sqrt{5+x^{2}}, y_{2}=-\sqrt{5+x^{2}}$

D) $y_{1}=\sqrt{5-x^{2}}, y_{2}=-\sqrt{5-x^{2}}$

Accepted Answer

The answer of The circle or ellipse shown in the...

Question 11

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given?
-$\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$

A) $y_1=5 \sqrt{1+\frac{x^{2}}{16}}, y_2=-5 \sqrt{1+\frac{x^{2}}{16}}$

B) $\mathrm{y}_{1}=5 \sqrt{1-\frac{\mathrm{x}}{4}}, \mathrm{y}_{2}=-5 \sqrt{1-\frac{\mathrm{x}}{4}}$

C) $y_{1}=5 \sqrt{1-\frac{x^{2}}{16}}, y_{2}=-5 \sqrt{1-\frac{x^{2}}{16}}$

D) $y_{1}=5 \sqrt{1-\frac{x^{2}}{4}}, y_{2}=-5 \sqrt{1-\frac{x^{2}}{4}}$

Accepted Answer

The answer of The circle or ellipse shown in the...

Question 12

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given?
-$(x-5)^{2}+y^{2}=25$

A) $y_{1}=\sqrt{25-(x-5)^{2}}, y_{2}=-\sqrt{25-(x-5)^{2}}$

B) $y_{1}=5+\sqrt{x-5}, y_{2}=5-\sqrt{x-5}$

C) $y_{1}=25+\sqrt{x-5}, y_{2}=25-\sqrt{x-5}$

D) $y 1=\sqrt{25+(x-5)^{2}}, y 2=-\sqrt{25+(x-5)^{2}}$

Accepted Answer

The answer of The circle or ellipse shown in the...

Question 13

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given?
-$(x-1)^{2}+(y-1)^{2}=1$

A) $y_{1}=-1+\sqrt{1-(x-1)^{2}}, y_{2} =-1-\sqrt{1-(x-1)^{2}}$

B) $y_{1}=-1+\sqrt{1-(x-1)^{2}}, y_{2}=1-\sqrt{1-(x-1)^{2}}$

C) $\mathrm{y}_{1}=1+\sqrt{1-(\mathrm{x}-1)^{2}}, \mathrm{y}_{2}=1-\sqrt{1-(\mathrm{x}-1)^{2}}$

D) $y_{1}=1+\sqrt{1-(x-1)^{2}}, y_{2}=-1-\sqrt{1-(x-1)^{2}}$

Accepted Answer

The answer of The circle or ellipse shown in the...

Question 14

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given?
-$(x-2)^{2}+(y-2)^{2}=1$

A) $\mathrm{y}_{1}=2+\sqrt{1+(\mathrm{x}-2)^{2}}, \mathrm{y}_{2}=2-\sqrt{1+(\mathrm{x}-2)^{2}}$

B) $\mathrm{y}_{1}=\sqrt{1-(\mathrm{x}-2)^{2}}, \mathrm{y}_2=-\sqrt{1-(\mathrm{x}-2)^{2}}$

C) $\mathrm{y}_{1}=2+\sqrt{1-(\mathrm{x}-2)^{2}}, \mathrm{y}_{2}=2-\sqrt{1-(\mathrm{x}-2)^{2}}$

D) $y_{1}=2+\sqrt{(x-2)^{2}-1}, y_{2}=2-\sqrt{(x-2)^{2}-1}$

Accepted Answer

The answer of The circle or ellipse shown in the...

Question 15

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given?
-$x^{2}+\frac{(y+5)^{2}}{25}=1$

A) $y_{1}=5+5 \sqrt{1+x^{2}}, y_{2}=5-5 \sqrt{1+x^{2}}$

B) $y_{1}=-5+5 \sqrt{1+x^{2}}, y_{2}=-5-5 \sqrt{1+x^{2}}$

C) $y_{1}=5+5 \sqrt{1-x^{2}}, y_{2}=5-5 \sqrt{1-x^{2}}$

D) $y_{1}=-5+5 \sqrt{1-x^{2}}, y_{2}=-5-5 \sqrt{1-x^{2}}$

Accepted Answer

The answer of The circle or ellipse shown in the...

Question 16

Solve the problem.
-An elliptical riding path is to be built on a rectangular piece of property that measures $6 \mathrm{mi}$ by $4 \mathrm{mi}$. Find an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{mi}$, if the path is to touch the center of the property line on all 4 sides.

A) $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$

B) $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

C) $\frac{x^{2}}{4}+\frac{y^{2}}{36}=1$

D) $\frac{x^{2}}{36}+\frac{y^{2}}{4}=1$

Accepted Answer

The answer of Solve the problem.
-An elliptical riding path is...

Question 17

Solve the problem.
-A railroad tunnel has the shape of half an ellipse. The height of the tunnel at the center is $52 \mathrm{ft}$ and the vertical clearance must be $26 \mathrm{ft}$ at a point $24 \mathrm{ft}$ from the center. Find an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{ft}$.

A) $\frac{x^{2}}{768}+\frac{y^{2}}{676}=1$

B) $\frac{x^{2}}{576}+\frac{y^{2}}{2704}=1$

C) $\frac{x^{2}}{2704}+\frac{y^{2}}{768}=1$

D) $\frac{x^{2}}{768}+\frac{y^{2}}{2704}=1$

Accepted Answer

The answer of Solve the problem.
-A railroad tunnel has the...

Question 18

Solve the problem.
-A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius 589 $\mathrm{km}$. Determine an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{km}$, if the distance of the satellite from the surface of the moon varies from $864 \mathrm{~km}$ to $174 \mathrm{~km}$.

A) $\frac{x^{2}}{1453}+\frac{y^{2}}{763}=1$

B) $\frac{x^{2}}{763^{2}}+\frac{y^{2}}{1453^{2}}=1$

C) $\frac{x^{2}}{864^{2}}+\frac{y^{2}}{174^{2}}=1$

D) $\frac{x^{2}}{174}+\frac{y^{2}}{864}=1$

Accepted Answer

The answer of Solve the problem.
-A satellite is to be...

Question 19

Solve the problem.
-A rectangular board is 8 by 20 . How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.
A) 9.2
B) .8
C) 4.0
D) 6.0

Accepted Answer

The foci are located at the ends of the major axis, which is the longest diameter of the ellipse. The major axis is perpendicular to the minor axis, which is the shortest diameter of the ellipse. The center of the ellipse is the midpoint of the major axis. The distance from the center of the ellipse to a focus is half the length of the major axis. The length of the major axis is 20 + 8 = 28. Therefore, the distance from the center of the ellipse to a focus is 28/2 = 14. Rounding to the nearest tenth, the distance from the center of the board to the foci is 14.1.

Question 20

Solve the problem.
-A rectangular board is 8 by 14 . The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.
A) 16
B) 8
C) 28
D) 14

Accepted Answer

The answer of Solve the problem.
-A rectangular board is 8...

Quiz 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Graph the circle. - $x^{2}+(y-3) ^{2}=16$ $Graph the circle. - x^{2}+(y-3) ^{2}=16 A) B) C) D)$

Graph the circle. - $(x-5) ^{2}+y^{2}=9$ $Graph the circle. - (x-5) ^{2}+y^{2}=9 A) B) C) D)$

Graph the circle. - $x^{2}+y^{2}-8 x-8 y+7=0$ $Graph the circle. - x^{2}+y^{2}-8 x-8 y+7=0 A) B) C) D)$

Graph the circle. - $x^{2}+y^{2}+2 x+8 y+8=0$ $Graph the circle. - x^{2}+y^{2}+2 x+8 y+8=0 A) B) C) D)$

Graph the circle. - $2 y^{2}=32-2 x^{2}$ $Graph the circle. - 2 y^{2}=32-2 x^{2} A) B) C) D)$

Graph the ellipse. - $\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$ $Graph the ellipse. - \frac{x^{2}}{4}+\frac{y^{2}}{49}=1 A) B) C) D)$

Graph the ellipse. - $\frac{(x+5) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+5) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1 A) B) C) D)$

Graph the ellipse. - $\frac{(x+1) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+1) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1 A) B) C) D)$

Solve the problem. -A rectangular board is 8 by 20 . How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

Solve the problem. -A rectangular board is 8 by 14 . The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.

Quiz 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Graph the circle. - x2+(y−3) 2=16x^{2}+(y-3) ^{2}=16x2+(y−3) 2=16

Graph the circle. - (x−5) 2+y2=9(x-5) ^{2}+y^{2}=9(x−5) 2+y2=9

Graph the circle. - x2+y2−8x−8y+7=0x^{2}+y^{2}-8 x-8 y+7=0x2+y2−8x−8y+7=0

Graph the circle. - x2+y2+2x+8y+8=0x^{2}+y^{2}+2 x+8 y+8=0x2+y2+2x+8y+8=0

Graph the circle. - 2y2=32−2x22 y^{2}=32-2 x^{2}2y2=32−2x2

Graph the ellipse. - x24+y249=1\frac{x^{2}}{4}+\frac{y^{2}}{49}=14x2​+49y2​=1

Graph the ellipse. - (x+5) 29+(y−1) 24=1\frac{(x+5) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=19(x+5) 2​+4(y−1) 2​=1

Graph the ellipse. - (x+1) 29+(y−1) 24=1\frac{(x+1) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=19(x+1) 2​+4(y−1) 2​=1

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions y1y_{1}y1​ and y2y_{2}y2​ that were used to obtain the graph whose equation is given? - x2+y2=25x^{2}+y^{2}=25x2+y2=25

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions y1y_{1}y1​ and y2y_{2}y2​ that were used to obtain the graph whose equation is given? - (x−5) 2+y2=25(x-5) ^{2}+y^{2}=25(x−5) 2+y2=25

Solve the problem. -A rectangular board is 8 by 20 . How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

Solve the problem. -A rectangular board is 8 by 14 . The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.

Graph the circle. - $x^{2}+(y-3) ^{2}=16$ $Graph the circle. - x^{2}+(y-3) ^{2}=16 A) B) C) D)$

Graph the circle. - $(x-5) ^{2}+y^{2}=9$ $Graph the circle. - (x-5) ^{2}+y^{2}=9 A) B) C) D)$

Graph the circle. - $x^{2}+y^{2}-8 x-8 y+7=0$ $Graph the circle. - x^{2}+y^{2}-8 x-8 y+7=0 A) B) C) D)$

Graph the circle. - $x^{2}+y^{2}+2 x+8 y+8=0$ $Graph the circle. - x^{2}+y^{2}+2 x+8 y+8=0 A) B) C) D)$

Graph the circle. - $2 y^{2}=32-2 x^{2}$ $Graph the circle. - 2 y^{2}=32-2 x^{2} A) B) C) D)$

Graph the ellipse. - $\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$ $Graph the ellipse. - \frac{x^{2}}{4}+\frac{y^{2}}{49}=1 A) B) C) D)$

Graph the ellipse. - $\frac{(x+5) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+5) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1 A) B) C) D)$

Graph the ellipse. - $\frac{(x+1) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+1) ^{2}}{9}+\frac{(y-1) ^{2}}{4}=1 A) B) C) D)$