# How do you write an equation for a circle given center (-8,-7) and tangent to the y-axis?

Oct 9, 2016

${\left(x + 8\right)}^{2} + {\left(y + 7\right)}^{2} = 64$

#### Explanation:

The standard form of the equation of a circle is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where (a ,b) are the coordinates of the centre and r, the radius.

here centre = (-8 ,-7) $\Rightarrow a = - 8 \text{ and } b = - 7$

Since the y-axis is a tangent then the radius will be the horizontal distance from (-8 ,-7) to the y-axis ( x = 0). That is radius = 8.

substitute values into the standard equation.

${\left(x - \left(- 8\right)\right)}^{2} + {\left(y - \left(- 7\right)\right)}^{2} = {8}^{2}$

$\Rightarrow {\left(x + 8\right)}^{2} + {\left(y + 7\right)}^{2} = 64 \text{ is the equation of the circle}$
graph{(x+8)^2+(y+7)^2=64 [-31.6, 31.6, -15.8, 15.8]}