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Let PQ be a focal chord of the parabola ...

Let PQ be a focal chord of the parabola `y^(2)=4ax`. The tangents to the parabola at P and Q meet at point lying on the line
`y=2x+a,alt0`.
If chord PQ subtends an angle `theta` at the vertex of `y^(2)=4ax`, then `tantheta=`

A

`2sqrt(7)//3`

B

`-2sqrt(7)//3`

C

`2sqrt(5)//3`

D

`-2sqrt(5)//3`

Text Solution

Verified by Experts

The correct Answer is:
D
4 Angle made by chord PQ at vertex (0,0) is given by
`tantheta|(m_(OP)-m_(OQ))/(1+m_(OP)*m_(OQ))|((2//t)+2t)/(1-4)=(2{(1//t)+t})/(-3)=(-2sqrt(5))/(3)`
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