How to Convert a Polar Equation to Cartesian Form?

[qablos]

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"...

 

[Dick]

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.

 

[qablos]

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?

 

[haruspex]

I feel it's slightly clearer as (a²-x²)/2a, but your answer is fine.