Parabola Ques 8

Passage

Let $P Q$ be a focal chord of the parabola $y^2=4 a x$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y=2 x+a, a>0$.

(2013 Adv.)

  1. Length of chord $P Q$ is

(a) $7 a$

(b) $5 a$

(c) $2 a$

(d) $3 a$

Show Answer

Answer:

Correct Answer: 8.(b)

Solution: (b) Since, $R\left[-a, a\left(t-\frac{1}{t}\right)\right]$ lies on $y=2 x+a$.

$\Rightarrow \quad a \cdot\left(t-\frac{1}{t}\right)=-2 a+a \Rightarrow t-\frac{1}{t}=-1$

Thus, length of focal chord

$ =a\left(t+\frac{1}{t}\right)^2=a\left\{\left(t-\frac{1}{t}\right)^2+4\right\}=5 a $



Table of Contents