Question

Find parametric equations for x²+y²−4y=0.

Answer 1

x = 2cosθ , y = 2 + 2sinθ

Explanation:

x² + y² - 4y = 0

complete the square on the y- term

add( half the coefficient of the y- term )² to both sides

x² + y² + 2(- 2)y + 4 = 0 + 4

x² + (y - 2)² = 4 = r²

then r =
`√(4)` = 2

x = rcosθ = 2cosθ

y - 2 = rsinθ = 2sinθ

y = 2 + 2sinθ