All the points (1, 0), ( - 1, 0) , (2, 0) and (5, 0) lie on the x -axis. Reason : Equation of the x -axis is y = 0.
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Asked on November 22, 2019 by
Vindhya Chakravarty
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.
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ANSWER
Since O is the centre of the circle and A,B are points on its circumference.
∴OA=OB=Radius
⇒OA=OB
⇒
(2+1)
2
+(−3y−y)
2
=
(2−5)
2
+(−3y−7)
2
⇒9+16y
2
=9+(3y+7)
2
⇒16y
2
=9y
2
+42y+49
⇒7y
2
−42y−49=0
⇒y
2
−6y−7=0
⇒(y−7)(y+1)=0⇒y=−1,7
When y=-1: The coordinates of O,A and B are O(2,3), A(-1,-1) and B(5,7) respectively.
∴Radius=OA=
(2+1)
2
+(3+1)
2
=5
When y=7: The coordinates O,A and B are O(2,-21), A(-1,7) and B(5,7) respectively.
∴Radius=OA=
(2+1)
2
+(−21−7)
2
=
9+784
=