Question

The normals at three points P, Q, and R of the parabola \( y^2 = 4ax \) meet at \( (h, k) \). The centroid of the triangle formed by the points P, Q, and R lies on?

• A. \( x = 0 \)
• B. \( y = 0 \)
• C. \( x = -a \)
• D. \( y = a \)

Hint:

For parabolas, the centroid of a triangle formed by normals lies on specific axes depending on the geometry of the curve.

Answer 1

The Correct Option is B

Using the properties of the parabola and the condition that the normals at P, Q, and R meet at the point \( (h, k) \), we find that the centroid of the triangle formed by the points lies on the line \( y = 0 \).