Question

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

Answer 1

`(x-3)^2+(y+1)^2=9`

or `x^2+y^2-6x+2y+1=0` in quadratic form.

Explanation:

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

`(x-3)^2+(y-(-1))^2=3^2`

or `(x-3)^2+(y+1)^2=9`

or `x^2-6x+9+y^2+2y+1=9`

or `x^2+y^2-6x+2y+1=0`