# How do you find the equation of the circle, center C(4,-8), tangent to the y-axis?

Jan 29, 2016

${\left(x - 4\right)}^{2} + {\left(y + 8\right)}^{2} = 16$

#### Explanation:

The equation of a circle is : ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

(a , b ) are the coordinates of the centre and r , the radius.

The centre is given ( 4 , -8 ) . Require the radius r .

Since the y-axis is a tangent then the distance from centre

to the y-axis is 4 units. Hence r = 4 .

equation is : ${\left(x - 4\right)}^{2} + {\left(y + 8\right)}^{2} = {4}^{2}$

${\left(x - 4\right)}^{2} + {\left(y + 8\right)}^{2} = 16$