Explore BrainMass

# Conic Sections in Polar Coordinates

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

(a)
Also, we have (1)
Pl is parallel to the x-axis, so Pl = DE (2)
And (3)
Substitute (2) and (3) to equation (1), we have
Therefore,

Then PF = r
According to the definition of e, we have , so

(*)

The conversion between the polar and rectangular coordinates is
(4)
Therefore, (5)
Square both sides of equation (*), we have
(6)
Substitute equations (4) and (5) to (6)

(7)
When e <1, , so , that is, the coefficient of is greater than 0. so it is an equation of ellipse.

When e > 1, , equation (7) is
, so it is an equation of hyperbola.

https://brainmass.com/math/calculus-and-analysis/conic-sections-polar-coordinates-133116

#### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

4. The conversion between the polar and rectangular coordinates is
(1)
Therefore, (2)
Given that:
Cross-multiplying,
r + r e cos = ed, or r = ...

#### Solution Summary

Conic Sections in Polar Coordinates are investigated.

\$2.19