Question

(x²+y²)²=2 x y Convert the equation to polar coordinates and simplify.

Answer 1

To convert the equation (x²+y²)²=2xy to polar coordinates, substitute x = rcos(θ) and y = rsin(θ) into the equation, simplify, and use the trigonometric identity cos²(θ) + sin²(θ) = 1.

Step-by-step explanation:

To convert the equation (x²+y²)²=2xy to polar coordinates, we can use the relationships x = rcos(θ) and y = rsin(θ). Substituting these values into the equation and simplifying:

(r²cos²(θ) + r²sin²(θ))² = 2(rcos(θ))(rsin(θ))

Expanding and simplifying further:

r⁴(cos²(θ) + sin²(θ))² = 2r²cos(θ)sin(θ)

Since cos²(θ) + sin²(θ) = 1, the equation becomes:

r⁴ = 2r²cos(θ)sin(θ)