Question

The number of distinct normals that can be drawn from $(-2,1)$ to the parabola $y^2-4x-2y-3=0$, is

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is A $1$

Here, $y^2-2y+1=4(x+1)$
$\Rightarrow (y-1{)}^2=4(x+1)$.
So, the axis is $y-1=0$.
Also, $(-2,1)$ lies on the axis of parabola and it is exterior to the parabola because $1^2-4(-2)-2\left(1\right)-3=4>0.$

Hence, only one normal is possible.