Question

The locus of the point of intersection of two tangents to the parabola y²=4ax, which are at right angle to one another is

• A. \(x^2+y^2=a^2\)
• B. \(ay^2=x\)
• C. \(x+a=0\)
• D. x+y+a=0

Hint:

For parabola y²=4ax, perpendicular tangents intersect on the directrix.

Answer 1

The Correct Option is C

Step 1: Equation of tangent with slope m: y=mx+(a)/(m)
Step 2: For perpendicular tangents, m₁m₂=-1.
Step 3: Solving intersection gives x=-a.