Question

What is the center of the circle given by the equation `(x + 5)^2 + (y - 8)^2 = 1`?

Answer 1

The centre of the circle is `(-5,8)`

Explanation:

The basic equation of a circle centred on the point `(0,0)` is `x^2 + y^2 = r^2` when `r` is the radius of the circle.

If the circle is moved away to some point `(h,k)` the equation becomes `(x-h)^2 + (y-k)^2 = r^2`

In the given example `h = -5` and `k = 8`

The centre of the circle is therefore `(-5,8)`