# The curve $a^{2}y^{2}=x^{2}(a^{2}-x^{2})$ has

(1)only one loop between$x=0$ and $x=a$(2)two loops between $x=0$ and $x=a$(3)two loops between $x=-a$ and $x=a$(4)no loop

The curve $a^2y^2=x^2(a^2-x^2)$ has one loop between -a ad 0.
The curve has two loops between -a and a
Hence 3 is the correct answer.