Question

If three distinct normals can be drawn to the parabola $y^2-2y=4x-9$ from the point $(2a,b)$ then find the range of the value of $a$.

Answer 1

$y^2-2y=4x-9$

$\therefore y^2-2y+1-1=4x-9$

$=(y-1{)}^2=4x-9+1$

$\therefore (y-1{)}^2=4(x-2)$

$\therefore a=1$

$\Rightarrow 2a>4$

$\therefore a>2$

Thus range of values of a is a $ϵ(2,\infty )$