Find the $y$-intercepts of the graph of the circle below.
$$( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36$$
A) $5 + 4 \sqrt { 2 } , 5 - 4 \sqrt { 2 }$
B) $5 + 2 \sqrt { 10 } , 5 - 2 \sqrt { 10 }$
C) $2 + \sqrt { 61 } , 2 - \sqrt { 61 }$
D) $- 2 + \sqrt { 11 } , - 2 - \sqrt { 11 }$
E) $- 2 + \sqrt { 61 } , - 2 - \sqrt { 61 }$

Question

Quizplus · Accepted Answer

To find the $y$-intercepts of the circle, set $x=0$ in the equation $(x-5)^2 + (y+2)^2 = 36$. This gives $(0-5)^2 + (y+2)^2 = 36$, which simplifies to $25 + (y+2)^2 = 36$. Solving for $y$ gives $y = -2 \pm \sqrt{11}$, which corresponds to choice D.

Find The yyy -Intercepts of the Graph of the Circle Below (x−5)2+(y+2)2=36( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36(x−5)2+(y+2)2=36

Find The $y$ -Intercepts of the Graph of the Circle Below $( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36$