Question

How do you graph `r=12/(-4costheta+6sintheta)`?

Answer 1

Draw a line with a `y`-intercept of `2` and a gradient of `2/3`

Explanation:

Multiply each term by `(-4costheta+6sintheta)`

`r(-4costheta+6sintheta)=12`

`-4rcostheta+6rsintheta=12`

`-2rcostheta+3rsintheta=6`

`rcostheta=x`
`rsintheta=y`

`-2x+3y=6`
`y=(2x+6)/3=(2x)/3+2`

Draw a line with a `y`-intercept of `2` and a gradient of `2/3`

Answer 2

I use the Desmos Graphing Calculator; it is a free online graphing tool that anyone can use.

Explanation:

One thing that I do not like about the calculator is that it requires that polar equations be in the form `r = f(theta)`; it will graph your equation very well but it will not graph something like the following:

`r^2 = r sin(theta) + 5`

It does not have this requirement for Cartesian equations.

I like that you can graph multiple equations and you can select the colors that you like.

I wish that it did 3d plots but you can't have everything for free.

You can make a user-id and I have one but I found that you have all of the features except the ability to save your work without logging on.