Question

The equation of the curve which passes through the point (1, 1) and whose slope is given by $\frac{2y}{x}$, is

• A. $y=x^2$
• B. $x^2-y^2=0$
• C. $2x^2+y^2=3$
• D. $Noneofthese$

Answer 1

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

Slope $\frac{dy}{dx}=\frac{2y}{x}$
$\Rightarrow 2\int \frac{dx}{x}=\int \frac{dy}{y}\Rightarrow 2logx=logy+logc\Rightarrow x^2=ye$
Since it passes through (1, 1), therefore c =1
Hence $x^2-y=0\Rightarrow y=x^2$.