Question

The locus of the mid-points of the focal chord of the parabola \( y^2 = 4ax \) is:

• A. \( y^2 = a(x - a) \)
• B. \( y^2 = 2a(x - a) \)
• C. \( y^2 = 4a(x - a) \)
• D. None of these

Hint:

For parabolas, the locus of the mid-points of the focal chord follows a specific geometric relation.

Answer 1

The Correct Option is B

Step 1: Understand the geometry of the parabola.
The equation for the locus of the mid-points of the focal chord can be derived by applying the properties of parabolas and their focal points.
Step 2: Conclusion.
Thus, the correct equation is \( y^2 = 2a(x - a) \).
Final Answer: \[ \boxed{y^2 = 2a(x - a)} \]