Question

the center of a circle is at $(-2, -7)$ and its radius is $6$.
what is the equation of the circle?
$\bigcirc\\ (x + 2)^2 + (y + 7)^2 = 36$
$\bigcirc\\ (x + 2)^2 + (y + 7)^2 = 3$
$\bigcirc\\ (x - 2)^2 + (y - 7)^2 = 3$
$\bigcirc\\ (x - 2)^2 + (y - 7)^2 = 36$

Explanation:

Step1: Recall the standard form of the circle equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Substitute the given values

Given \(h=-2\), \(k = - 7\), \(r = 6\).
Substitute into the formula: \((x-(-2))^2+(y-(-7))^2=6^2\).
Simplify to get \((x + 2)^2+(y + 7)^2=36\).

Answer:

\((x + 2)^2+(y + 7)^2=36\) (the first option)