I know how to prove it using polar coordinates. Using the parameters and , then . Using these substitutions, we can rewrite the equation you gave as:
Taking the square root of both sides gives you:
Dividing through r gives you:
Which finally gives us:
Now, notice when , . When , the representation on the Cartesian coordinate system is the curve going through the origin. Knowing this, you can say that the remaining intercept is . To show algebraically that has to be an intercept, refer back to the equation . Plugging in , you get: . The solution to that is , or simply the point .