Question

How do you graph `r=4+6costheta`?

Answer 1

See Socratic graph for the Cartesian form of the equation.

Explanation:

This limacon passes through the pole.

The pole is a dimple.

As `r = f(costheta)=f(cos(-theta)`, the graph is symmetrical about

`theta = 0`.

Maximum `r = f(0)=f(2pi)=10`.

I have used the Cartesian form of the polar equation.

`x^2+y^2-4sqrt(x^2+y^2)-6x=0`.

graph{x^2+y^2-4sqrt(x^2+y^2)-6x=0 [-20, 20, -10, 10]}