Question

Let the line $4x+3y+1=0$ meets the parabola $8y^2=ax$ at $P,Q$. If the angle made by chord $PQ$ at the vertex of the parabola in $90°$, then $|a|=$

Answer 1

Given line
$4x+3y+1=0\Rightarrow 1=-(4x+3y)$
For the given parabola the vertex will be origin
Hence the pair of lines joinig the vertex to the intersection point of line and parabola will be
$8y^2=a(-4x-3y)x\Rightarrow 8y^2+4a{x}^2+3axy=0$
For the pair of line to make right angle at origin
$\text{coefficient of}{x}^2+\text{coefficient of}{y}^2=0\Rightarrow a=-2$