# Question #65a2a

##### 1 Answer

Apr 16, 2017

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

intersection coordinates are

#### Explanation:

Our Polar equation is:

# r = 1+2cos theta#

To convert from polar to rectangular (Cartesian) coordinates we use the fundamental relationship:

# {: (x = rcos theta), (y = rsin theta) :} \ \ # and# \ \ x^2+y^2 = r^2 #

So we can transform our equation as follows:

# r = 1+2cos theta#

# :. r^2 = r + 2rcos theta#

# :. x^2+y^2 = sqrt(x^2+y^2) + 2x#

For the interaction with a unit circle which would have the equation:

# x^2+y^2 = 1 #

We would have:

# :. 1 = 1 + 2x => 2x =0 #

# " " => x=0#

And:

# x=0 => y^2 = 1 #

# " " => y = +-1 #

So the intersection coordinates would be