Find the length of a radius of each circle. Match each of the equations with length of a radius to obtain a true statement.
-$r = \sqrt { 19 }$
A) $x ^ { 2 } + y ^ { 2 } = 3$
B) $x ^ { 2 } + y ^ { 2 } + 14 x + 6 y + 39 = 0$
C) $x ^ { 2 } + y ^ { 2 } - 12 x + 20 y + 101 = 0$
D) $x ^ { 2 } + y ^ { 2 } + 24 x - 32 y = 0$

Question

Find the length of a radius of each circle. Match each of the equations with length of a radius to obtain a true statement.
-$r = \sqrt { 19 }$ 
A) $x ^ { 2 } + y ^ { 2 } = 3$ 
B) $x ^ { 2 } + y ^ { 2 } + 14 x + 6 y + 39 = 0$ 
C) $x ^ { 2 } + y ^ { 2 } - 12 x + 20 y + 101 = 0$ 
D) $x ^ { 2 } + y ^ { 2 } + 24 x - 32 y = 0$

Quizplus · Accepted Answer

The equation of a circle is given by:$$x^2 + y^2 + 2gx + 2fy + c = 0$$where (g, f) are the coordinates of the center and r is the radius.For the given equation:$$x^2 + y^2 + 14x + 6y + 39 = 0$$Comparing it with the standard equation, we get:$$g = -7, f = -3$$Therefore, the radius is:$$r = \sqrt{g^2 + f^2} = \sqrt{(-7)^2 + (-3)^2} = \sqrt{58} = \sqrt{19}$$

Find the Length of a Radius of Each Circle r=19r = \sqrt { 19 }r=19​

Find the Length of a Radius of Each Circle $r = \sqrt { 19 }$