Question

Check out the symmetry of this curve
${a}^{2} {y}^{2} = {x}^{2} ( {a}^{2} - {x}^{2} )$
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Answer 1

Answer:

${a}^{2} {y}^{2} = {x}^{2} ( {a}^{2} - {x}^{2} )$

Because of all even power of x and y the curve is symmetrical about both X axis and Y Axis.

Answer 2

Answer:

Because of all even power of X and Y the curve is symmetrical about both X axis and Y axis....

that is why

a^2y^2=x^2(a^2-y^2)