document.write( "Question 851372: What are the intersection points (at least three ordered par solutions) between a circle and parabola with equations X^2 + y^2 + 2x - 4y + 1 = 0 and y^2 - 2x - 4y - 2 = 0 ? \n" ); document.write( "

Algebra.Com's Answer #513218 by Fombitz(32388) $\"\"$ $\"About$

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$\"x%5E2+%2B+y%5E2+%2B+2x+-+4y+%2B+1+=+0\"$
\n" ); document.write( " $\"x%5E2%2B2x%2B1%2By%5E2-4y%2B4%2B1-1-4=0\"$
\n" ); document.write( "1. $\"%28x%2B1%29%5E2%2B%28y-2%29%5E2=4\"$
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\n" ); document.write( " $\"y%5E2-2x-4y-2=0\"$
\n" ); document.write( " $\"2x=y%5E2-4y%2B4-2-4\"$
\n" ); document.write( "2. $\"2x=%28y-2%29%5E2-6\"$
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\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"%28y-2%29%5E2=2x%2B6\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"%28x%2B1%29%5E2%2B%282x%2B6%29=4\"$
\n" ); document.write( " $\"x%5E2%2B2x%2B1%2B2x%2B6=4\"$
\n" ); document.write( " $\"x%5E2%2B4x%2B3=0\"$
\n" ); document.write( " $\"%28x%2B1%29%28x%2B3%29=0\"$
\n" ); document.write( " $\"x%2B1=0\"$
\n" ); document.write( " $\"x=-1\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"%28y-2%29%5E2=2%28-1%29%2B6\"$
\n" ); document.write( " $\"%28y-2%29%5E2=4\"$
\n" ); document.write( " $\"y-2=0+%2B-+2\"$
\n" ); document.write( " $\"y=0\"$ and $\"y=4\"$
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\n" ); document.write( " $\"x%2B3=0\"$
\n" ); document.write( " $\"x=-3\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"%28y-2%29%5E2=2%28-3%29%2B6\"$
\n" ); document.write( " $\"y-2=0\"$
\n" ); document.write( " $\"y=2\"$
\n" ); document.write( "So then the intersection points are (-1,0), (-1,4), (-3,2)\r
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