Q. 21 - Geometry

Question

Write an equation of the circle that has the given center and radius.$C(3,0);r=8$

Step-by-Step Solution

Answer

The equation of the circle is${\left(x-3\right)}^2+y^2=64$

Step-1 – Given

The given center = C(3, 0) and radius = r = 8.

Step-2 – To determine

We have to find the equation of the circle.

Step-3 – Calculation

Given that center = (a, b) = (3, 0) and radius = r = 8.

We will plug them in the standard form of a circle formula to get the equation:

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

$\begin{array}{l}{\left(x-3\right)}^2+{\left(y-0\right)}^2={\left(8\right)}^2\\ {\left(x-3\right)}^2+y^2=64\end{array}$

So, the equation of the circle is ${\left(x-3\right)}^2+y^2=64$.