Question

Write the equation of the circle centered at (−10,−7) with radius 13.

Answer 1

Given:

• Center of circle, (h, k) : (-10, -7)

,

• Radius, r = 13

Let's find the equation of the circle.

Apply the general form of the equation of a cirlce:

$(x-h)^2+(y-k)^2=r^2$

Where:

(h, k) is the center of the circle = (-10, -7)

r is the radius = 13

Thus, substitute -10 for h, -7 for k and 13 for r:

$\begin{gathered} (x-(-10))^2+(y-(-7))^2=13^2 \\ \\ (x+10)^2+(y+7)^2=169 \end{gathered}$

Therefore, the equation of the circle is:

$(x+10)^2+(y+7)^2=169$

ANSWER:

$(x+10)^{2}+(y+7)^{2}=169$