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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 a point lying on the line `y = 2x + a, a > 0`. Length of chord PQ is

A

7a

B

5a

C

2a

D

3a

Text Solution

Verified by Experts

The correct Answer is:
B
2 Since PQ is focal chord, let `P-=(at^(2),2at)andQ-=(a//t^(2),-2a//t)`.
We know that point of intersection of tangents at `P(t_(1))andQ(t_(2))" is "(at_(1)t_(2),a(t_(1)+t_(2)))`
`:. "The point of intersection of tangents at P and Q is "(-a,a(t-(1)/(t)))`
As the point of intersection lies on y=2x+a, we have
`a(t-(1)/(t))=-2a+a`
`or1-(1)/(t)=-1`
`or(t+(1)/(t))^(2)=5`
`:." Length of focal chord "PQ=a(t+(1)/(t))=5a`
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