Question

Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y). Find the values of y.

Answer 1

The given points are A(-1, y) , B(5,7)  and  O(2, -3y).

Here, AO and BO are the radii of the circle. So

AO = BO ⇒ AO² = BO²

`⇒ (2+1)^2+(-3-y)^2 = (2-5)^2 +(-3y-7)^2`

`⇒ 9+(4y)^2 = (-3)^2 +(3y+7)^2`

`⇒9+16y^2=9+9y^2 +49+42y`

`⇒ 7y^2 -42y^2 -49=0`

`⇒y^2 -6y-7=0`

`⇒y^2-7y+y-7=0`

`⇒y(y-7)+1(y-7)=0`

`⇒(y-7)(y+1)=0`

`⇒y=-1or y =7`

Hence , y=7 or y=-1