Question

A variable chord $PQ$ of the parabola $y^2=4x$ is drawn parallel to the line $y=x$. If the parameters of the points $P$ & $Q$ on the parabola are $p$ & $q$ respectively, then $p+q=$

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

Equation of chord parallel to $y=x$ is given by, $y=x+c$
Let it intersect the parabola $y^2=4x$ at $(t^2,2t)$
$\Rightarrow 2t=t^2+c\Rightarrow t^2-2t+c=0$ (i)
Given parameters at point $P$ and $Q$ are $p$ and $q$
$\therefore p+q=$ sum of roots of (i) $=2$