If the normals at `P(t_(1))andQ(t_(2))` on the parabola meet on the same parabola, then

Question

If the normals at `P(t_(1))andQ(t_(2))` on the parabola meet on the same parabola, then

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`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

5 views Answered 2023-02-05 15:29