Finding Cartesian Equations for Curves Given in Polar Coordinates

Typically a curve is given in polar coordinateswithas a function ofIt is often quite simple to write this in cartesian coordinatesby making the substitutionsand simplifying the resulting expression.


On substituting these, the equation becomes

Subtract the terms on the right hand side to give

We can complete the square for both the's and's to giveThis is the equation of a circle with centreand radius 2. Note thatsatisfies the cartesian equation so lies on the curve.