Question

The family of curves in which the subtangent at any point to any curve is double the abscissa is given by

(A) $x=C y^2$

(B) $y=C x^2$

(C) $x^2=C y^2$

(D) $y^2=\mathrm{Cx}{ }^2$

Answer 1

Explain :

The length of subtangent $=y \cdot \frac{d x}{d y}$

Given, $\quad y \frac{d x}{d y}=2 x \Rightarrow \frac{d x}{x}=2 \frac{d y}{y}$

$\Rightarrow \quad \log x=2 \log y+\log C \Rightarrow x=C y^2$

So, The correct option is (A).