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Points A(-1, Y) and B(5,7) Lie on the Circle with Centre O(2, -3y).Find the Value of Y. - Mathematics

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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 ⇒ AO= 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

Concept: Coordinate Geometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 1

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