Question:
<p>If tangents drawn to the parabola (x - 1)<sup>2</sup> = 8(y + 1) which are perpendicular to the variable line y = px - 2p<sup>2</sup> - p - 1, where p is a parameter, then point of these tangents to the variable line lie on the curve, which is:</p>
<p style="display:inline">y + 3 = 0</p>
<p style="display:inline">x = 3</p>
<p style="display:inline">x + 3 = 0</p>
<p style="display:inline">y = 3</p>
Step-by-Step Solution
Key Concept: The locus of the intersection point of two perpendicular tangents to a parabola is always its directrix.
<p>y + 3 = 0</p>
Correct Answer: A