Question:medium

Through the vertex \(O\) of parabola \(y^2=4x\), chords OP and OQ are drawn at right angles to one another. The locus of the midpoint of PQ is

Show Hint

Use parametric form for locus problems in conics.

Updated On: Mar 24, 2026

\(y^2=2x+8\)
\(y^2=x+8\)
\(y^2=2x-8\)
\(y^2=x-8\)

Show Solution

The Correct Option is D

Solution and Explanation

Was this answer helpful?

0

Top Questions on sections of a cone

Let P be a point on the parabola, \( x^2 = 4y \). If the distance of P from the centre of the circle, \( x^2 + y^2 + 6x + 8 = 0 \) is minimum, then the equation of the tangent to the parabola at P, is :
- BITSAT - 2026
- Mathematics
- sections of a cone
View Solution
If two tangents from point \((h,k)\) to parabola \(y^2 = 64x\) have slopes such that one is 8 times the other, then value of \( \frac{k^2}{2h} \) is:
- MET - 2024
- Mathematics
- sections of a cone
View Solution
The eccentricity of the conic \(9x^2 - 16y^2 = 144\) is
- MET - 2021
- Mathematics
- sections of a cone
View Solution
The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity would be
- BITSAT - 2021
- Mathematics
- sections of a cone
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in BITSAT exam

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is:

BITSAT - 2026
Relative Velocity

If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :

BITSAT - 2026
Definite Integral

If \( x = \sqrt{2^{\text{cosec}^{-1} t}} \) and \( y = \sqrt{2^{\text{sec}^{-1} t}} (|t| \ge 1) \), then dy/dx is equal to :

BITSAT - 2026
Derivatives of Functions in Parametric Forms

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately 0.530 \AA. The radius for the first excited state (n = 2) orbit is (in \AA)

BITSAT - 2026
Bohr's model of hydrogen atom