Question
Question: Consider a focal chord PQ of the parabola y<sup>2</sup> = 4ax, a∈ R<sup>+</sup>. Tangent drawn at P ...
Consider a focal chord PQ of the parabola y2 = 4ax, a∈ R+. Tangent drawn at P and normal drawn at Q meet the axis of the parabola at T and N respectively. Let P be (at2, 2at). If angle between PT and QN is ‘α’ and distance between PT and QN is ‘d’, then
A
d = 
B
00<α< 900
C
d = 0
D
None of these
Answer
d =
Explanation
Solution
PQ is the focal chord so that co-ordinates of P and Q are (at2, 2at) and (a/t2, –2a/t) respectively.
Since the tangents at P and Q to the parabola re perpendicular to each other,
PT and QN are parallel ⇒ α = 00
Also, d =
=.