Question

Write an equation of the circle that has the given center and radius.

$C(0,0);r=6$

Short answer

The equation of the circle is $x^2+y^2=36$.

Step-by-step solution

Step-1 – Given

The given center = C(0, 0) and radius = r = 6.

Step-2 – To determine

We have to find the equation of the circle.

Step-3 – Calculation 

Given that center = (a, b) = (0, 0) and radius = r = 6.

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

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

$\begin{array}{l}{\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(6\right)}^2\\ x^2+y^2=36\end{array}$

So, the equation of the circle is$x^2+y^2=36.$