Question

In the following exercises, write the standard form of the equation of the circle with the given radius and center

Radius: $10,$center: $(-2,6)$

Short answer

The standard form of the equation of the circle is${(x+2)}^2+{(y-6)}^2=100.$

Step-by-step solution

Step 1. Given Information

The given radius is$10$ and the center is$(-2,6).$

We have to write the standard form of the equation of the circle with the given radius and center.

Step 2. Use the standard form of the equation of a circle

The standard form of the equation of a circle is ${(x-h)}^2+{(y-k)}^2=r^2.$

Now, substitute the given values in the equation $r=10$and $h=-2,k=6$

role="math" localid="1645193549342" $$\begin{gathered} {(x+2)}^2+{(y-6)}^2={10}^2 \\ {(x+2)}^2+{(y-6)}^2=100 \end{gathered}$$