Question

For the parabola $y^2 = 4ax,$ then ratio of the subtangent to the abscissa is

• A. $1 : 1$
• B. $2 : 1$
• C. $x : y$
• D. $x^2 : y.$

Answer 1

Answer: (B)

$2 : 1$

Answer 2

$y^2 = 4ax$ $\Rightarrow 2\,y \frac{dy}{dx} = 4a$ $\Rightarrow \frac{dy}{dx} = \frac{2a}{y}$ Subtangent $= \frac{y}{dy / dx}=\frac{y}{2\, a/y}$ $= \frac{y^{2}}{2a} = \frac{4ax}{2a}= 2x$ $\therefore \frac{\text{Subtangent}}{x} = \frac{2}{1}$ Hence reqd. ratio is $2 : 1$.