Question

write the standard form of the equation of the circle with the given center and radius. center (-3,7), r = 2 type the standard form of the equation of the circle. (simplify your answer.)

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of the equation of a circle 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 \(h=-3\), \(k = 7\), and \(r = 2\).
Substitute into \((x - h)^2+(y - k)^2=r^2\):
\((x-(-3))^2+(y - 7)^2=2^2\)

Step3: Simplify the equation

\((x + 3)^2+(y - 7)^2=4\)

Answer:

\((x + 3)^2+(y - 7)^2=4\)