Find the equation of the circle

Question

Find the equation if the circle with the center at the point $(-2,5)$ and tangent to the line $x=7$.

My teacher gives us the answer of $(x+2)^2+(y-5)^2=81$. I just wanna know the solution (another methods) that will help me understands better

Answer 1

Line from centre to a tangent is $ \perp$ at the point of tangency

Since $x=7$ is a vertical line then $r=7-(-2)=9$ and $C(-2,5)$

$(x+2)^2+(y-5)^2=9^2$

Answer 2

As $x=7$ is tangent to the circle with center at $(-2,5)$, the perpendicular distance from the center to $x=7$ will be the circle's radius.

Here radius $= r = |-2-7| = 9$ units.

Then, the equation of circle with center $(a,b)$ and radius $r$ units is,

$(x-a)^2+(y-b)^2 = r^2$