Question

points A (-1,y) and B (5,7) lie on a circle with centre C (2,-3y). Find the radius of the circle

Answer 1

Here, CB=CA=Radius

So, CB²=CA²

By applying distance formula,

(5-2)² + (7+3y)² = (-1-2)² + (y+3y)²

⇒9+49+9y²+42x = 9+16y²

⇒7y²-42y-49=0

⇒7y²-49y+7y-49=0

⇒7y(y-7)+7(y-7)=0

⇒(7y+7)(y-7)=0

Therefore, 7y+7=0                 or             y-7=0

                 y=-1                        or            y=7

Case 1: (y=-1)

Radius=CB=√(5-2)²+(7-3)²=5 units.

Case 2: (y=7)

Radius=CB=√(5-2)²+(7+21)²=√793 units.(Ans.)