# What is the standard form of the equation of a circle with centre (3,-1) and which touches the y-axis?

Aug 1, 2018

${\left(x - 3\right)}^{2} + {\left(y + 1\right)}^{2} = 9$

or ${x}^{2} + {y}^{2} - 6 x + 2 y + 1 = 0$ in quadratic form.

#### Explanation:

As circle with center $\left(3 , - 1\right)$ touches $y$-axis, its radius is equal to its abscissa i.e. $3$, and hence standard form of the equation of circle is

${\left(x - 3\right)}^{2} + {\left(y - \left(- 1\right)\right)}^{2} = {3}^{2}$

or ${\left(x - 3\right)}^{2} + {\left(y + 1\right)}^{2} = 9$

or ${x}^{2} - 6 x + 9 + {y}^{2} + 2 y + 1 = 9$

or ${x}^{2} + {y}^{2} - 6 x + 2 y + 1 = 0$