Question

convert the polar equation r^2=2cos^2theta + 3sin^2theta into a rectangular equation

Answer 1

Multiply both sides by r^2:
r^4=r^2(2cos^2(theta)+3sin^2(theta))
(r^2)^2=2(r*cos(theta))^2+3(r*sin(theta)^2
(x^2+y^2)^2=2x^2+3y^2