Question

How do you find the equation of a circle with center at the point (-8,5) and tangent to the x-axis?

Answer 1

`(x+8)^2+(y-5)^2=5^2`

Explanation:

A circle with center `(x_c,y_c)` tangent to the x-axis has a radius, `r`, equal to the distance from the center to the x-axis, namely `y_c`.

The general formula for a circle with center `(x_c,y_c)` and radius `r` is
`color(white)("XXX")(x-x_c)^2+(y-y_c)^2=r^2`

For the given values `(x_c,y_c)=(-8,5)`
and derived value `r=5`
this gives us:
`color(white)("XXX")(x+8)^2+(y-5)^2=5^2`
graph{(x+8)^2+(y-5)^2=25 [-16.86, 5.64, -1.03, 10.22]}