Final answer:
To convert the equation (xy)^2 = 7 to polar coordinates, you substitute the Cartesian coordinates with polar equivalents, resulting in the polar equation r^4 = 7.
Step-by-step explanation:
To convert the equation (xy)^2 = 7 into polar coordinates, we start by using the relationships between Cartesian coordinates (x, y) and polar coordinates (r, θ): x = r cos θ and y = r sin θ. By substituting these expressions into the original equation, we get:
(r cos θ * r sin θ)^2 = 7
which simplifies to:
(r^2 * cos θ * sin θ)^2 = 7
By taking a square root on both sides, we can simplify further:
r^4 * (cos θ * sin θ)^2 = r^4
Given that the original equation includes r^4, we isolate this term and equate it to 7:
r^4 = 7
This is the converted equation in polar coordinates.