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.