Question

Equation of the curve passing through (1, 1) and having gradient $\frac{2y}{x}(x>0,y>0)$ is:

• A. $xy=1$
• B. $2x+y=3$
• C. $x=y^2$
• D. $y=x^2$

Answer 1

The correct option is D $y=x^2$

$\frac{dy}{dx}={}^{2y}{/}_x$
$\Rightarrow \int \frac{dy}{y}=\int \frac{2dx}{x}+logc$
$\Rightarrow logy=log{x}^{2}c$
$\Rightarrow y=c{x}^2$
Put $(x,y)=(1,1)$
$\Rightarrow 1=c\times 1\Rightarrow c=1$
$\Rightarrow y=x^2$