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Question: The normal at P on y<sup>2</sup> = 4ax meets the curve again in Q. If y<sub>1</sub>, y<sub>2</sub> a...

The normal at P on y2 = 4ax meets the curve again in Q. If y1, y2 are the ordinates of P and the mid point of PQ, then y1y2 =

A

a2

B

-a2

C

4a2

D

-4a2

Answer

-4a2

Explanation

Solution

If P = t1 and Q = t2

t2 = -t1 - Qt1\frac{Q}{t_{1}}

Then by given data y1 = 2at1

y2=a(t1+t2)y_{2} = a(t_{1} + t_{2})

=a(−2t1)==−2ay1/2a=−4a2y1= a\left( \frac{- 2}{t_{1}} \right) = = \frac{- 2a}{y_{1}/2a} = \frac{- 4a^{2}}{y_{1}}⇒ y1y2=−4a2y_{1}y_{2} = - 4a^{2}