Question

Convert r= 5/ 1+3sinθ to a rectangular equation

Answer 1

Given:

`r=(5)/(1+3\sin \theta)`

Find: Rectangular equation.

Sol:

`r^2=x^2+y^2`
`\begin{gathered} y=r\sin \theta \\ \sin \theta=(y)/(r) \end{gathered}`
`\begin{gathered} r=(5)/(1+3\sin \theta) \\ r=(5)/(1+(3y)/(r)) \end{gathered}`
`\begin{gathered} r=(5r)/(r+3y) \\ r+3y=5 \\ r=5-3y \\ r^2=(5-3y)^2 \end{gathered}`

Put the value in rectangular equation:

`\begin{gathered} x^2+y^2=r^2 \\ x^2+y^2=(5-3y)^2 \end{gathered}`