Chapter 10 - Conics, Parametric Equations, and Polar Coordinates - 10.4 Exercises - Page 722: 35

Rectangular form: $x^2 + y^2 -3y = 0$ Graph:

**Remember: $cos^2(θ) + sin^2(θ) = 1$, $rcos(θ) = x$ and $rsin(θ) = y$ $r = 3sin(θ)$ Multiply both sides by "r": $r * (r) = (3sin(θ)) * r$ $r^2 = 3rsin(θ)$ $(1)r^2 = 3y$ $(cos^2(θ) + sin^2(θ))r^2 = 3y$ $r^2cos^2(θ) + r^2sin^2(θ) = 3y$ $x^2 + y^2 = 3y$: $x^2 + y^2 -3y = 0$