Question

How do you graph `r = 2 /( 1- sintheta)`?

Answer 1

Draw a graph of `y=x^2` that is lowered by 4 units and have all `y`-values quartered (squished by x4)

Explanation:

Multiply each side by `r(1-sintheta)` to get:
`r^2-r^2sintheta=2r`

`r^2-r(rsintheta)=2r`

`r^2=x^2+y^2`
`r=sqrt(x^2+y^2)`
`rsintheta=y`

`x^2+y^2-ysqrt(x^2+y^2)=2sqrt(x^2+y^2)`

`x^2+y^2=sqrt(x^2+y^2)(2+y)`

`2+y=(x^2+y^2)/sqrt(x^2+y^2)=sqrt(x^2+y^2)`

`4+4y+y^2=x^2+y^2`

`y=(x^2-4)/4`

Draw a graph of `y=x^2` that is lowered by 4 units and have all `y`-values quartered (squished by x4):
graph{(x^2-4)/4 [-5, 5, -2, 5]}