Question

Question #0f0cb

Answer 1

`(x^2 +y^2)^3= 9(x^2 -y^2)^2`

Explanation:

Write the given equation as `r=3(cos^2 theta - sin^2 theta)`

Or `r^3= 3 (r^2 cos^2 theta -r^2 sin^2 theta)`

Since `r^2 = x^2 +y^2` and `rcos theta =x, and rsin theta =y`,

it would be `(x^2+y^2)^(3/2) = 3(x^2- y^2)`

Now square both sides. `(x^2 +y^2)^3= 9(x^2 -y^2)^2`