Question:
<p>Locus of the point of intersection of the tangents at the ends of the normal chords of the parabola y<sup>2</sup> = 4ax is :</p>
<p style="display:inline">(x + 2a)y<sup>2</sup> + 4a<sup>2</sup> = 0</p>
<p style="display:inline">(2a + x)y<sup>2</sup> + 4a<sup>3</sup> = 0</p>
<p style="display:inline">(x + 3a)y<sup>3</sup> - 4a<sup>2</sup> = 0</p>
<p style="display:inline">(x + 2a)y<sup>2</sup> + 4a<sup>3</sup> = 0</p>
Step-by-Step Solution
Key Concept: Combine the parametric coordinates of the tangent intersection point with the normal chord condition t2 = -t1 - 2/t1 to eliminate the parameters.
<p>(2a + x)y<sup>2</sup> + 4a<sup>3</sup> = 0</p>
Correct Answer: B