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

Algebra.Com's Answer #524534 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!

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\n" ); document.write( "Yes, it's straightforward.
\n" ); document.write( " $\"x=Rcos%28theta%29\"$
\n" ); document.write( " $\"y=Rsin%28theta%29\"$
\n" ); document.write( " $\"x%5E2%2By%5E2=%28Rcos%28theta%29%29%5E2%2B%28Rsin%28theta%29%29%5E2=R%5E2\"$ <--- That's the real simplifier.
\n" ); document.write( "So then,
\n" ); document.write( " $\"%28x%5E2%2By%5E2%29=%28x%5E2%2By%5E2-x%29%5E2\"$
\n" ); document.write( "becomes
\n" ); document.write( " $\"R%5E2=%28R%5E2-Rcos%28theta%29%29%5E2\"$
\n" ); document.write( " $\"R=R%5E2-Rcos%28theta%29\"$
\n" ); document.write( " $\"R%281%2Bcos%28theta%29%29=R%5E2\"$
\n" ); document.write( " $\"highlight_green%28R=1%2Bcos%28theta%29%29\"$
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\n" ); document.write( "When $\"theta=0\"$ , $\"R=2\"$
\n" ); document.write( "When $\"theta=90\"$ , $\"R=1\"$
\n" ); document.write( "When $\"theta=180\"$ , $\"R=0\"$
\n" ); document.write( "When $\"theta=270\"$ , $\"R=1\"$
\n" ); document.write( "And finally back to $\"t=360\"$ , $\"R=2\"$
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\n" ); document.write( "Once you have $\"R\"$ and $\"theta\"$ , you can convert back to x and y to plot.
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