Q38 of 66 Page 7

Points A(-1,y) and B(5,7) lie on a circle with centre O(2,-3y). Find the values of y. Hence, find the radius of the circle. (CBSE 2014) 

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 + (-3y-y)2 = (2-5)2 + (-3y-7)2

⇒ 9 + (4y)2 = (-3)2 +(3y+7)2

⇒ 9 + 16y2 = 9 +9y2 + 49 + 42y

⇒ 7y2 – 42y – 49 = 0

⇒ y2 – 6y – 7 = 0

⇒ y2 – 7y + y – 7 = 0

⇒ y(y-7) + 1(y-7) = 0

⇒ (y +1)(y-7) = 0

Hence y = 7 , y = -1

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