Question

The length of subnormal at any point to the parabola $y^2=4ax$ is -

• A. $1$
• B. $2$
• C. $2a$
• D. $4a$

Answer 1

The correct option is C $2a$

$y^2=4ax$ and any point on this curve be $(x_1,y_1)$
Thus, slope of tangent at $(x_1,y_1)$ is
${\left(\frac{dy}{dx}\right)}_{(x_1,y_1)}=\left(\frac{2a}{y_1}\right)$
$\therefore$ The length of subnormal is $\Rightarrow y_1.{\left(\frac{dy}{dx}\right)}_{(x_1,y_1)}$
$\Rightarrow y_1.\frac{2a}{y_1}\Rightarrow 2a$
Hence, option 'C' is correct.