Question

X²+y²=4 x+4 y Convert the equation to polar coordinates and simplify.

Answer 1

To convert the equation to polar coordinates, substitute x = rcosθ and y = rsinθ into the equation and simplify.

Step-by-step explanation:

To convert the equation to polar coordinates, we can substitute x = rcosθ and y = rsinθ into the equation. This gives us (rcosθ)² + (rsinθ)² = 4rcosθ + 4rsinθ. Simplifying this equation, we get r²(cos²θ + sin²θ) = 4rcosθ + 4rsinθ. Since cos²θ + sin²θ = 1, the equation becomes r² = 4rcosθ + 4rsinθ.