Question

How do you graph `r=4costheta-2`?

Answer 1

This is a circle with center at `(2,0)` and radius `sqrt2`. It's equation in rectangular form is `x^2+y^2-4x+2=0`.

Explanation:

To graph `r=4costheta-2` let us convert it into rectangular coordinates.

The relation between polar coordinates `(r,theta)` and rectangular coordinates `(x,y)` are given by `x=rcostheta` and `y=rsintheta` and hence `r=sqrt(x^2+y^2)`

Hence `r=4costheta-2` is nothing but

`rxxr=4costhetaxxr-2r` or

`x^2+y^2=4x-2sqrt(x^2+y^2)` or

graph{x^2+y^2=4x-2sqrt(x^2+y^2) [-4, 4, -2, 2]}

Answer 2

See the graph below

Explanation:

The graph looks like this: