Question

what is the equation, in standard form, of a circle with center $(-5,-9)$ and radius 7? enter your answer by filling in the boxes. $(xsquare )^{2}+(ysquare )^{2}=square$

Explanation:

Step1: Recall the standard form of a circle's 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 center and radius

Given \(h=-5\), \(k = - 9\), \(r = 7\).
For the \(x\) - part: \(x-(-5)=x + 5\).
For the \(y\) - part: \(y-(-9)=y + 9\).
For the right - hand side: \(r^2=7^2 = 49\).

Answer:

\((x + 5)^2+(y + 9)^2=49\)