Question

The family of curves, in which the subtangent of 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. $y=cx$

Answer 1

The correct option is A $x=c{y}^2$

Suntangent $=\frac{y}{m}=\frac{y}{\frac{dy}{dx}}=2x$ (given)
$\Rightarrow \frac{2dy}{y}=\frac{dx}{x}\Rightarrow 2\log y=\log x+\log c$

$\Rightarrow \log y^2=\log cx\Rightarrow y^2=ck$

$\Rightarrow x=c{y}^2$

Hence, option A.