# Conic Sections in Polar Coordinates

Not what you're looking for?

(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.

##### Purchase this Solution

##### Solution Summary

Conic Sections in Polar Coordinates are investigated.

##### 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 = ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Probability Quiz

Some questions on probability

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.