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.)
- 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 is determined by the distance from the focus to the directrix
$ a\left(t+\frac{1}{t}\right)^2=a\left(t-\frac{1}{t}\right)^2+4=a\left(2+\frac{2}{t^2}\right)=5 a $
BETA
