Question

Let PQ be a focal chord of the parabola $y^2=4x$. The tangents to the parabola at P and Q meet at a point on
y = 2x + 1.

Length of chord PQ is

• A. 4
• B. 3
• C. 5
• D. 7

Answer 1

The correct option is C 5

$P=(t^2,2t),Q=(\frac{1}{t^2},\frac{-2}{t})\therefore t-\frac{1}{t}=-1\Rightarrow t+\frac{1}{t}=\sqrt{5}\to PQ=a{(t+\frac{1}{t})}^2=5\to tan\theta =\frac{2(\frac{1}{t}+t)}{1-4}=\frac{2\sqrt{5}}{3}$