Question

Convert the Cartesian equation x^2 + y^2 + 3y = 0 to a polar equation.r^2 = -3 sin θr = √3 sin θr = -3 sin θ

Answer 1

From the question

`x^2+y^2+3y=0`

This becomes

`(x^2+y^2)+3y=0`

In polar,

`\begin{gathered} x^2+y^2=r^2 \\ \\ \text{and } \\ \\ y=r\sin \theta \end{gathered}`

So, this becomes

`\begin{gathered} r^2+3r\sin \theta=0 \\ \\ (r^2)/(r)=(-3r\sin \theta)/(r) \\ \\ r=-3\sin \theta \end{gathered}`