Question

The length of subtangent of the curve $y^2=4x$ at point $(1,-2)$ is __________.

• A. $-2$
• B. $2$
• C. $1$
• D. $3$

Answer 1

The correct option is B $2$

$y^2=4x$
$\therefore 2y\frac{dy}{dx}=4$
$\therefore \frac{dy}{dx}=\frac{2}{y}$
$\therefore {\left(\frac{dy}{dx}\right)}_{P(1,-2)}=\frac{2}{-2}=-1$
Length of sub-tangents $=\left|\frac{y_1}{{\left(\frac{dy}{dx}\right)}_{x_1,y_1}}\right|$
$=\left|\frac{-2}{-1}\right|$
$=2$.