Converting a Conic Section Equation from Polar Form to Rectangular Form

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Convert the equation r=6/(2−4 cos⁡θ ) into an equation written in rectangular form.

We convert equations from polar form to rectangular form using the following relationships.

To go from polar to rectangular coordinates:

To go from rectangular to polar coordinates:

We can use the relationship above to convert conic sections that are given in polar form into a rectangular equation.

[jamesstrickland]

That isn't necessary a hyperbola because of the 4 out front. It's because it is greater than the 2. Had it been 5-4cos then it would have been an ellipse.