Question

Circle O has a center of (-1,5) and passes through the point (2,9) write the equation in center radius form and standard form

Answer 1

Firstly, calculate the radius r of the circle using distance between two points

$\begin{gathered} r\text{ = }\sqrt[]{(2-(-1))2+(9-5)^2} \\ r=\text{ }\sqrt[]{(2+1)^2+(4)^2} \\ r=\sqrt[]{3^2+4^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=\text{ 5} \end{gathered}$

Then use the radius r=5 and the center (-1 , 5) to find the equation of the circle

$\begin{gathered} r^2=(x-h)^2+(y-k)^2 \\ 5^2=(x-(-1))^2+(y-5)^2 \\ 5^2=(x+1)^2+(y-5)^2 \end{gathered}$

The center radius form is

$5^2=(x+1)^2+(y-5)^2$

The standard form is

$\text{ 25}^{}=(x+1)^2+(y-5)^2$