Question

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

• A. 7a
• B. 5a
• C. 2a
• D. 3a

Answer 1

The correct option is B 5a



Since, $R[-a,a(t-\frac{1}{t})]$ lies on $y=2x+a$
$\Rightarrow a\cdot (t-\frac{1}{t})=-2a+a\Rightarrow t-\frac{1}{t}=-1$
Thus, length of focal chord
$=a{(t+\frac{1}{t})}^2=a\{{(t-\frac{1}{t})}^2+4\}=5a$