Question

Number of real normals to the parabola $y^2=16x,$ passing through $(4,0)$ is

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is A $1$

Eqaution of the normal to the parabola $y^2=16x$ will be
$y+xt=8t+4t^3$
$\because$ it passes through $(4,0)$
$\therefore 4t=8t+4t^3\Rightarrow 4t^3+4t=0\Rightarrow t(t^2+1)=0$
$\therefore$ only one value of $t(=0)$ is possible.
Hence one normal can be drawn.