Question

How do you convert `r(2 + cos theta) = 1` to rectangular form?

Answer 1

3 x.x + 4 y.y + 2 x -1 = 0 or in the standard form for the equation of an ellipse ( x + 1/3 )^2 / (1/3) + y^2 / (1/2) = 1

Explanation:

The polar equation is (1/2) / r = 1 + (1/2) cos `theta`. This represents an ellipse with semi-major axis 2/3 and eccentricity 1/2. The pole is a focus and the polar center is ( 1/3, `pi` ) or the equivalent ( `-`1/3, 0 )