How to Convert a Polar Equation to Cartesian Form?

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    Cartesian Form
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Homework Help Overview

The discussion revolves around converting a polar equation, specifically r(1+sinθ)=a, into Cartesian form. Participants are exploring the relationships between polar and Cartesian coordinates.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conversion process using the relationships x=rcosθ and y=rsinθ, as well as the equation r²=x²+y². There is a focus on the challenge of eliminating the variable "a" from the equation.

Discussion Status

Some participants suggest that the original poster may have reached a satisfactory form of the equation, while others offer alternative expressions for clarity. There is an ongoing exploration of different ways to represent the final equation.

Contextual Notes

There is a mention of the difficulty in eliminating "a" from the equation, which may indicate constraints in the problem setup or assumptions about the variables involved.

qablos
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Find the Cartesian Form of

r(1+sinθ)=a
I understand that:
x=rcosθ
y=rsinθ
and r2=x2+y2I can get quite far to the point I end up with

x2=a2-2ay

I'm struggling to eliminate "a"...
 
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qablos said:
Find the Cartesian Form of

r(1+sinθ)=a



I understand that:
x=rcosθ
y=rsinθ
and r2=x2+y2


I can get quite far to the point I end up with

x2=a2-2ay

I'm struggling to eliminate "a"...

You can't eliminate a. I think you are already done.
 
Dick said:
You can't eliminate a. I think you are already done.

Okay...I've expressed my answer as:

y=1/2[a-(x2/a)]

Is that a better way to express it?
 
I feel it's slightly clearer as (a2-x2)/2a, but your answer is fine.
 

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