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