Question

If normal is drawn to $y^2=12x$ making an angle ${45}^o$ with the axis then the foot of the normal is

• A. $(3,8)$
• B. $(3,-6)$
• C. $(12,-12)$
• D. $(8,-8)$

Answer 1

Answer: (A)

$(3,8)$

Given that,

$y^2=12x--\left(1\right)$

Diff. w.r.t. to $x$

$2y\frac{dy}{dx}=12$

$y\frac{dy}{dx}=6----\left(2\right)$

Slope tangent

$\frac{dy}{dx}=\tan 45$

$m=1$

Slope at Normal from $\left(2\right)$

$\Rightarrow y\left(-1\right)=6$

$\Rightarrow y=-6$

$\therefore x=3$

Point $=(3,-6)$

Option $\left(A\right)$ is correct answer.