Question

What is the standard form of the equation of a circle with r = 5; (h, k) = (-5, 2)?

Answer 1

`(x+5)^2+(y-2)^2=25`

Explanation:

The standard form of the equation of a circle of radius `r` centered at the point `(h,k)` is `(x-h)^2+(y-k)^2=r^2`.

This equation is reflecting the fact that such a circle consists of all points in the plane that are distance `r` from `(h,k)`. If a point `P` has rectangular coordinates `(x,y)`, then the distance between `P` and `(h,k)` is given by the distance formula `sqrt{(x-h)^2+(y-k)^2}` (which itself comes from the Pythagorean Theorem).

Setting that equal to `r` and squaring both sides gives the equation `(x-h)^2+(y-k)^2=r^2`.