Question
Mathematics Question on Parabola
Let a tangent to the curve y2=24x meet the curve xy=2 at the points A and B Then the mid points of such line segments AB lie on a parabola with the
A
length of latus rectum 23
B
length of latus rectum 2
C
directrix 4x=3
D
directrix 4x=−3
Answer
directrix 4x=3
Explanation
Solution
The correct answer is (C) : directrix 4x=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