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Question

Mathematics Question on Parabola

Let a tangent to the curve y2=24xy^2=24 x meet the curve xy=2x y=2 at the points AA and BB Then the mid points of such line segments ABA B lie on a parabola with the

A

length of latus rectum 32\frac{3}{2}

B

length of latus rectum 2

C

directrix 4x=34 x =3

D

directrix 4x=34 x=-3

Answer

directrix 4x=34 x =3

Explanation

Solution

The correct answer is (C) : directrix 4x=34 x =3
y2=24x
a=6
xy=2
AB≡ty=x+6t2.......(1)
AB≡T=S1​
kx+hy=2hk.........(2)
From (1) and (2)
1k​=−th​=−6t22hk​
⇒ then locus is y2=−3x
Therefore directrix is 4x=3