Q. 20 - Geometry

Question

Find the center and radius of each circle.

${\left(x+a\right)}^2+{\left(y-b\right)}^2=c^2$

Step-by-Step Solution

Answer

The center is (-a, b) and the radius is c.

Step-1 – Given

The given equation is ${\left(x+a\right)}^2+{\left(y-b\right)}^2=c^2.$

Step-2 – To determine

We have to find the center and the radius of the given circle.

Step-3 – Calculation

We compare the given equation${\left(x+a\right)}^2+{\left(y-b\right)}^2=c^2$ with the standard form of a circle:${\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2$.

Here (a, b) is the center and r being the radius.

Comparing the two equations we get: a = - a, b = b and r = c.

So, the center is (- a, b) and the radius is c.