Question

$P$ and $Q$ are two distinct points on the parabola, $y^2 = 4x$, with parameters $t$ and $t_1$ respectively. If the normal at $P$ passes through $Q$, then the minimum value of $t^2_1$ is :

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (D)

8

Answer 2

$t _{1}=- t -\frac{2}{ t }$ $t _{1}^{2}= t ^{2}+\frac{4}{ t ^{2}}+4$ $\min$ of $t _{1}^{2}=8$