Question
Question: A tangent to the parabola y<sup>2</sup> = 4ax meets the x-axis in T and the tangent at the vertex A ...
A tangent to the parabola y2 = 4ax meets the x-axis in T and the tangent at the vertex A in P, If TAPQ is a rectangle, then the locus of Q is
A
y2 = 2ax
B
y2 = -ax
C
y2 = ax
D
x2 = -ay
Answer
y2 = 2ax
Explanation
Solution
The equation of tangent to the parabola at 't' is yt = x+at2.
Put y = 0 ⇒ x = -at2 ∴ T = (-at2, 0)
Put x = 0 ⇒ y = at ∴ P = (0, at)
Let Q = (x, y) then from figure (x, y) = (-at2, at)
⇒ y2 + ax = 0.