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If the normals at P(t(1))andQ(t(2)) on t...

If the normals at `P(t_(1))andQ(t_(2))` on the parabola meet on the same parabola, then (A) `t_(1)t_(2)=-1` (B) `t_(2)=-t_(1)-(2)/(t_(1))` (C) `t_(1)t_(2)=1` (D) `t_(1)t_(2)=2`

A

`t_(1)t_(2)=-1`

B

`t_(2)=-t_(1)-(2)/(t_(1))`

C

`t_(1)t_(2)=1`

D

`t_(1)t_(2)=2`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) Normal at point `P(t_(1))` meets the parabola again at point `R(t_(3))`.
Then `t_(3)=-t_(1)-(2)/(t_(1))`
Comparing these values of `t_(3)`, we have
`-t_(1)-(2)/(t_(1))=-t_(2)-(2)/(t_(2))`
`:." "t_(1)t_(2)=2`
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