# How do you write polar equations of hyperbolas, from the polar equations of their asymptotes?

##### 1 Answer

See the explanation. Details about easy to remember polar equations of asymptotes and hyperbola are included.

#### Explanation:

The polar equation of a straight line is

foot of the perpendicular from the pole r = 0, on the straight line.

So, the polar equation of hyperbolas having

as asymptotes is

Note that

For example, consider the asymptotes

Their polar equations are

So, the polar equations of the related hyperbolas are

Upon setting C = 1, this gives the hyperbola

that has the Cartesian form

and this in the standard form is

Graph for the illustrative hyperbola

graph{((x-1)^2-y^2-1)((x-1)^2-y^2)=0[-2 6 -2 2]}