Let T be the tangent to the parabola $\mathrm{y}^{2}=16 \mathrm{x}$ at the point (64, 32). Let L be the tangent to the same parabola at another point $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$ on the parabola. If L and T are perpendicular to each other, then the distance between the point $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$ and the focus of the parabola, is

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Parabola

Let T be the tangent to the parabola

y^{2} = 16 x

at the point (64, 32). Let L be the tangent to the same parabola at another point

(x_{1}, y_{1})

on the parabola. If L and T are perpendicular to each other, then the distance between the point

(x_{1}, y_{1})

and the focus of the parabola, is

Answer: (C)

For parabola

y^{2} = 16 x

, the tangent at

(64, 32)

32 y = 8 (x + 64)

, which simplifies to

x - 4 y + 64 = 0

with slope

\frac{1}{4}

. A perpendicular tangent has slope

- 4

. Using the parametric form

(4 t^{2}, 8 t)

and slope

\frac{1}{t} = - 4

, we get

t = - \frac{1}{4}

. Thus

P = (\frac{1}{4}, - 2)

. The focus is at

(4, 0)

. Distance

P F = (4 - \frac{1}{4})^{2} + 4 = \frac{225}{16} + \frac{64}{16} = \frac{289}{16} = \frac{17}{4}

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Single correct option