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Points A(-1, y) and B(5, 7) lie on a cir...

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

Text Solution

Verified by Experts

The correct Answer is:
y = 7 or y = -1
We know that the radii of a circle are equal.
`therefore OA = OB rArr OA^(2) = OB^(2)`
`rArr (2+1)^(2) + (-3y-y)^(2) = (2-5)^(2) + (-3y-7)^(2)`
`rArr 3^(2) + 16y^(2) = (-3)^(2) + (9y^(2) + 49 + 42y)`
`rArr 7y^(2) -42y -49 =0 rArr y^(2) -6y -7 = 0`
`rArr (y-7)(y+1) = 0 rArr y = 7 "or" y = -1`
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