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# An asymptote to the curve $y^{2}(a+2x)=x^{2}(3a-x)$ is

$\begin{array}{1 1}(1)x=3a&(2)x=-a/2\\(3)x=a/2&(4)x=0\end{array}$

Can you answer this question?

$y^2(a+2x)=x^2(3a-x)$
$y^2= \large\frac{x^2(3a-x)}{(a+2x)}$
If $x= \large\frac{-a}{2}$ then $y=\infty$
$\therefore x=-\large\frac{-a}{2}$ is an asymptote.
Hence 2 is the correct answer.
answered May 20, 2014 by