Q. 18 - Geometry

Question

Find the center and radius of each circle.

${\left(x+7\right)}^2+{\left(y-8\right)}^2=\frac{36}{25}$

Step-by-Step Solution

Answer

The center is (-7, 8) and the radius is $\frac{6}{5}$

Step-1 – Given

The given equation is${\left(x+7\right)}^2+{\left(y-8\right)}^2=\frac{36}{25}$

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 ${\left(x+7\right)}^2+{\left(y-8\right)}^2=\frac{36}{25}$

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 = - 7, b = 7 and r = $\frac{6}{5}$ .

So, the center is (-7, 8) and the radius is$\frac{6}{5}$ .