SOLUTION: Graph 𝑥^2+𝑦^2=(𝑥^2+𝑦^2−𝑥)^2. This is from the conics rotation of axes section. I understand the hyperbola and ellipse section. B

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Graph 𝑥^2+𝑦^2=(𝑥^2+𝑦^2−𝑥)^2. This is from the conics rotation of axes section. I understand the hyperbola and ellipse section. B      Log On


   



Question 869883: Graph 𝑥^2+𝑦^2=(𝑥^2+𝑦^2−𝑥)^2. This is from the conics rotation of axes section.
I understand the hyperbola and ellipse section. But I could really use some insight on this. THANKS TO ALL

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Yes, it's straightforward.
x=Rcos%28theta%29
y=Rsin%28theta%29
x%5E2%2By%5E2=%28Rcos%28theta%29%29%5E2%2B%28Rsin%28theta%29%29%5E2=R%5E2 <--- That's the real simplifier.
So then,
%28x%5E2%2By%5E2%29=%28x%5E2%2By%5E2-x%29%5E2
becomes
R%5E2=%28R%5E2-Rcos%28theta%29%29%5E2
R=R%5E2-Rcos%28theta%29
R%281%2Bcos%28theta%29%29=R%5E2
highlight_green%28R=1%2Bcos%28theta%29%29
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When theta=0, R=2
When theta=90,R=1
When theta=180,R=0
When theta=270,R=1
And finally back to t=360, R=2
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Once you have R and theta, you can convert back to x and y to plot.