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Q.

If A, B, C are 3 points in a parabola. 1, 2 are the areas of triangle is formed by the  points A, B, C and the tangents at A, B, C. If 1, 2are the roots of px2+qx+r=0 then condition is

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a

9q2=2pr 

b

9pr=2q2 

c

2p2=9qr

d

9p2=2qr 

answer is A.

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Detailed Solution

1=18ay1-y1 y2-y3 y3-y1 2=116ay1-y2 y2-y3 y3-y1 12=2   1+21-2=3    1+2=31-2 -qp=3 q2-4prp q2=9q2-36pr  8q2=36pr 2q2=9pr

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