Question

write the standard form of the equation of the circle with the given center and radius. center $(-3,5)$, $r = \sqrt{5}$ the equation of the circle in standard form is. (simplify your answer.)

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 values into the formula

Given \(h=-3\), \(k = 5\), and \(r=\sqrt{5}\).
Substitute into \((x - h)^2+(y - k)^2=r^2\):
\((x-(-3))^2+(y - 5)^2=(\sqrt{5})^2\)

Step3: Simplify the equation

\((x + 3)^2+(y - 5)^2=5\)

Answer:

\((x + 3)^2+(y - 5)^2=5\)