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If normal to parabola y^(2)=4ax at point...

If normal to parabola `y^(2)=4ax` at point `P(at^(2),2at)` intersects the parabola again at Q, such that sum of ordinates of the points P and Q is 3, then find the length of latus ectum in terms of t.

Text Solution

Verified by Experts

The correct Answer is:
`-3t`
Let parameter of point Q be t'.
`:." "t'=-t-(2)/(t)`
`rArr" "t+t'=-(2)/(t)`
`rArr" "2at+2at'=-(4a)/(t)=3` (given)
`rArr" "4a=-3t`
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