Question

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

• A. \(y^2=2x+8\)
• B. \(y^2=x+8\)
• C. \(y^2=2x-8\)
• D. \(y^2=x-8\)

Hint:

Use parametric form for locus problems in conics.

Answer 1

The Correct Option is D

Step 1: Parametric points on parabola: \[ P(at^2,2at),\; Q(as^2,2as) \]
Step 2: Condition of perpendicular chords gives relation between \(t\) and \(s\).
Step 3: Coordinates of midpoint satisfy: \[ y^2=x-8 \]