Question

The curve $9y^2=x^2(4-x^2)$ is symmetrical about

• A. $y$-axis
• B. $x$-axis
• C. $y=x$
• D. Both are axes

Answer 1

The correct option is D Both are axes

Given curve is $9y^2=x^2(4-x^2)$

$\Rightarrow 9y^2-x^2(4-x^2)=0$

Let $F(x,y)=9y^2-x^2(4-x^2)$

Now $F(-x,-y)=9(-y{)}^2-(-x{)}^2[4-(-x{)}^2]=9y^2(4-x^2)$

So given curve is symmetrical about both the axes