Question

the number of distinct normals that can be drawn from (2 - 1) to the parabola Y^2+ X + 2 Y + 2 =0
(A)0
(B)1
(C)2
(D)3

Answer 1

The given parabola is :

$y^2 + x + 2 y + 2=0 \\\\ (y+1)^2+x+1=0 \\\\ (y+1)^2 = -(x+1)$

As we can see that (2,-1) does not lie on the parabola.Because

LHS= 0

and , RHS = -3

As point (2,-1) lies outside the parabola, so two tangents can be drawn from point (2,-1).

As normal is a line perpendicular to tangent.

So, Number of distinct Normals from point (2,-1) = 2→→→→Option (C)