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If PQ and Rs are normal chords of the pa...

If PQ and Rs are normal chords of the parabola `y^(2) = 8x` and the points P,Q,R,S are concyclic, then

A

tangents at P and R meet on X-axis

B

tangents at P and R meet on Y-axis

C

PR is parallel to Y-axis

D

PR is parallel to X-axis

Text Solution

Verified by Experts

The correct Answer is:
A, C
Equation of normal chords at `P(2t_(1)^(2),4t_(1))` and `R(2t_(2)^(2),4t_(2))` are `y + t_(1)x -4t_(1) -2t_(1)^(3) =0`
and `y + t_(2) x - 4t_(2) - 2t_(2)^(3) =0`.
Equation of curve through, P,Q,R,S is
`(y + t_(1)x -4t_(1)-2t_(1)^(3)) (y + t_(2)x -4t_(2) -2t_(2)^(3)) + lambda (y^(2) - 8x) =0`
P,Q,R,S are concyclic, `t_(1) + t_(2) =0` and `t_(1)t_(2) =1 + lambda`. Thus, point of intersection of tangents i.e., `(at_(1)t_(2),a (t_(1)+t_(2))` lies on X-axis. Slope of `PR = (2)/(t_(1)+t_(2))`
Hence, PR is parallel to Y-axis.
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