Question

A circle passes A(-4,-1) and B(2,1). How do you find the center and radius of this circle if the center of the circle is on y-axis?

Answer 1

graph{x^2 +(y+3)^2=20 [-10, 10, -5, 5]}
Given that the center of the circle is on y-axis (`x=0`), let us consider the coordinates of its center `(O)` be `(0,a)`

So

`OA^2=OB^2=R^2`,Where R is the radius of the circle.

`4^2+(a+1)^2=2^2+(a-1)^2=R^2`

`=>(a+1)^2-(a-1)^2=2^2-4^2`

`=>4a=-12`

`=>a=-3`

Hence coordinates of the center (O) is (-3,0).

And radius `R=sqrt(2^2+(a-1)^2)`

`=>R=sqrt(2^2+(-3-1)^2)=2sqrt5`