# How do you find general form of circle with center is (2,-3) and passes through (2, 7)?

Jun 6, 2018

Equation of the circle is (x – 2)^2 + (y +3)^2 = 100

#### Explanation:

The center-radius form of the circle equation is

(x – h)^2 + (y – k)^2 = r^2, with the center being at the point

$\left(h = 2 , k = - 3\right)$ and the radius being $r$. The circle passes

through point $A \left(2 , 7\right) \mathmr{and} C \left(2 , - 3\right)$ is the center .

Distance formula is AC=r= sqrt ((x_1-x_2)^2+(y_1-y_2)^2

${r}^{2} = {\left(2 - 2\right)}^{2} + {\left(7 - \left(- 3\right)\right)}^{2} = 100$ Hence equation of the

circle is (x – 2)^2 + (y +3)^2 = 100

graph{(x-2)^2+(y+3)^2=100 [-40, 40, -20, 20]}