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Question: If y<sub>1</sub>, y<sub>2</sub> are the ordinates of two points P and Q on the parabola and y<sub>3<...

If y1, y2 are the ordinates of two points P and Q on the parabola and y3 is the ordinate of the point of intersection of tangents at P and Q, then

A

y1, y2, y3 are in A.P.

B

y1, y3, y2 are in A.P.

C

y1, y2, y3 are in G.P.

D

y1, y3, y2 are in G.P.

Answer

y1, y3, y2 are in A.P.

Explanation

Solution

P(x1, y1) Q(x2, y2)

Point of intersection of P and Q.

(x3, y3) = (x1x2,y1+y22)\left( \sqrt{x_{1}x_{2}},\frac{y_{1} + y_{2}}{2} \right)

\ y3 = y1+y22\frac{y_{1} + y_{2}}{2}̃ y1, y3, y2 are in A.P.