Question

What is the equation of the circle with a center at `(4 ,-3 )` and a radius of `5`?

Answer 1

`(x-4)^2+(y+3)^2=25`

Explanation:

The standard form of a circle with a center at `(h,k)` and a radius `r` is

`(x-h)^2+(y-k)^2=r^2`

Since the center is `(4,-3)` and the radius is `5`, we know that

`{(h=4),(k=-3),(r=5):}`

Thus, the equation of the circle is

`(x-4)^2+(y-(-3))^2=5^2`

This simplifies to be

`(x-4)^2+(y+3)^2=25`