# How do you graph the system of polar equations to solve #r=2+2costheta# and #r=3+sintheta#?

##### 1 Answer

See the graph for your pair of a cardioid and a limacon. I have used Socratic utility. Common points are

#### Explanation:

Here, use cartesian forms of the equations :

For the cardioid, it is from

and, for the limacon, it is from

It is revealed that one common point is on

We can measure the other angle or solve

For the second point, use

graph{(x^2+y^2-2sqrt(x^2+y^2)-2x)(x^2+y^2-3sqrt(x^2+y^2)-y)=0 [-10, 10, -5, 5]}