How do you find a polar equation that has the same graph as the given rectangular equation: x^2 - y^2 =1?

1 Answer
Apr 27, 2018

r^2=sec2x

Explanation:

The relation between polar coordinates (r,theta) and rectangular or Cartesian coordinates (x,y) is given by

x=rcostheta and y=rsintheta

Hence using these transformations, we can write

x^2-y^2=1 as

r^2cos^2x-r^2sin^2x=1

or r^2(cos^2x-sin^2x)=1

or r^2cos2x=1 or r^2=sec2x

The graph of the equation representing a hyperbola appears as

prepared using utility at desmos.comprepared using utility at desmos.com