Question

Write the standard form of the equation of the circle with a radius of $7$ and center $(2,-4)$.

Short answer

The equation of circle is ${(x-2)}^2+{(y+4)}^2=49$.

Step-by-step solution

Step 1. Given information.

The radius of the circle is $7$.

The center of the circle is $(2,-4)$.

We have to write the standard form of the equation of this circle.

Step 2. Write the standard form of the equation of the circle

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

Step 3. Substitute the values of radius and center

Put $(h,k)=(2,-4)$

$r=7$

The equation of the circle will be:

$$\begin{gathered} {(x-2)}^2+{(y-(-4\left)\right)}^2=7^2 \\ {(x-2)}^2+{(y+4)}^2=49 \end{gathered}$$