Question

If $P(-5,1)$ is one end of the focal chord $PQ$ of the parabola $x=y^2-8y+2,$ then the slope of the tangent at the other end is

Answer 1

Tangents at the end of focal chord are perpendicular to each other
Slope of tangent at $Q=$ Slope of normal at $P$
Slope of normal to $y^2=4ax$ at $P$ is $-t$
Given, $x=y^2-8y+2$
$(y-4{)}^2=(x+14)$
Any point on the parabola will be $(-14+\frac{t^2}{4},4+\frac{t}{2})$
On comparing it with $(-5,1)$, we get $t=-6$
$\therefore$ Slope of the normal at $P$ will be $=6$
Hence, Slope of tangent at $Q\equiv 6$