Question

A circle is centered at C(-5,4) and has a radius of 2, how do you find the equation of a concentric circle with half the radius?

Answer 1

`(x+5)^2+(y-4)^2=1`

Explanation:

A general circle centred at `(a,b)` and having radius `r` has equation `(x-a)^2+(y-b)^2=r^2`.

Hence the given circle has equation `(x+5)^2+(y-4)^2=4`.

By concentric circle I assume you mean a circle with the same centre point `(-5,4)`. Thus only the radius is different and is 1 unit.

Therefore the new equation will be `(x+5)^2+(y-4)^2=1`