SOLUTION: What is the rectangular form of this polar equation r=9/1-3cos(theta) ?

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Question 887661: What is the rectangular form of this polar equation r=9/1-3cos(theta) ?
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
What is the rectangular form of this polar equation r=9/1-3cos(theta) ?
Always substitute for trig functions first, then simplify.
Always wait till last to substitute for r.

r%22%22=%22%229%2F%281-3cos%28theta%29%29

Substitute x%2Fr for cos%28theta%29

r%22%22=%22%229%2F%281-3%28x%2Fr%29%29

r%22%22=%22%229%2F%281-3x%2Fr%29

Multiply right side by r%2Fr

r%22%22=%22%229red%28r%29%2F%281-3x%2Fr%29red%28r%29

r%22%22=%22%229r%2F%28r-3x%29

Multiply both sides by %28r-3x%29

r%28r-3x%29%22%22=%22%229r

Divide both sides by r

r-3x%22%22=%22%229

r%22%22=%22%223x%2B9

Finally we substitute sqrt%28x%5E2%2By%5E2%29 for r

sqrt%28x%5E2%2By%5E2%29%22%22=%22%223x%2B9

Square both sides:

x%5E2%2By%5E2%22%22=%22%229x%5E2%2B54x%2B81

%220%22%22%22=%22%228x%5E2-y%5E2%2B54x%2B81

8x%5E2-y%5E2%2B54x%2B81%22%22=%22%22%220%22

Edwin