Question

write the equation of the circle centered at (-3, 2) with diameter 20.

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: Find the radius

Given diameter \(d = 20\), then radius \(r=\frac{d}{2}\). So \(r=\frac{20}{2}=10\).

Step3: Substitute the center \((h,k)=(-3,2)\) and radius \(r = 10\) into the standard form

Substitute \(h=-3\), \(k = 2\), and \(r = 10\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-3))^2+(y - 2)^2=10^2\), which simplifies to \((x + 3)^2+(y - 2)^2=100\).

Answer:

\((x + 3)^2+(y - 2)^2=100\)