Question

Convert the equation r=2/(1-sinθ) to rectangular form

Answer 1

`\displaystyle y=(x^2)/(4)-1`

Explanation:

`\displaystyle r=(2)/(1-\sin\theta)\\\\r-r\sin\theta=2\\\\√(x^2+y^2)-y=2\\\\√(x^2+y^2)=y+2\\\\x^2+y^2=y^2+4y+4\\\\x^2=4y+4\\\\(x^2)/(4)=y+1\\\\(x^2)/(4)-1=y`

Note that
`r=√(x^2+y^2)` and
`y=r\sin\theta`