Question

The straight line joining any point P on the parabola
y² = 4ax to the vertex and perpendicular from the focus to the tangent at P, intersect at R, then the equation of the locus of R is-

• A. 2x² + y² – 2ay = 0
• B. 2x² + y² – 2ax = 0
• C. 2x² + 2y² –ay = 0
• D. x² + 2y² –ax = 0

Answer 1

Answer: (B)

2x² + y² – 2ax = 0

Answer 2

P º (at², 2at), OP º y = $\frac{2}{t}$x

Equation of tangent at P ty = x + at²

R (h, k) lies on both k = $\frac{2}{t}$h ̃ t = $\frac{2h}{k}$

2$\frac{h}{k}$. k = h + a $\left( \frac{2h}{k} \right)^{2}$

Locus ̃ 2x² + y² –2ax = 0