document.write( "Question 843717: What are the centers of the equations and their points of intersection?
\n" ); document.write( "x^2=y+10
\n" ); document.write( "y^2+5(x-1)^2=81 \n" ); document.write( "

Algebra.Com's Answer #508495 by Fombitz(32388) $\"\"$ $\"About$

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Intersection of an ellipse and a parabola.
\n" ); document.write( "1. $\"x%5E2=y%2B10\"$
\n" ); document.write( "2. $\"y%5E2%2B5%28x-1%29%5E2=81\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"y=x%5E2-10\"$
\n" ); document.write( " $\"y%5E2=x%5E4-20x%5E2%2B100\"$
\n" ); document.write( "Substituting into eq. 2,
\n" ); document.write( " $\"x%5E4-20x%5E2%2B100%2B5%28x%5E2-2x%2B1%29=81\"$
\n" ); document.write( " $\"x%5E4-20x%5E2%2B100%2B5x%5E2-10x%2B5=81\"$
\n" ); document.write( " $\"%28x-1%29%28x-4%29%28x%2B2%29%28x%2B3%29=0\"$
\n" ); document.write( ".
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\n" ); document.write( "Four solutions:
\n" ); document.write( " $\"x-1=0\"$
\n" ); document.write( " $\"x=1\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"y=1%5E2-10=-9\"$
\n" ); document.write( "(1,-9)
\n" ); document.write( "and
\n" ); document.write( " $\"x-4=0\"$
\n" ); document.write( " $\"x=4\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"y=4%5E2-10=6\"$
\n" ); document.write( "(4,6)
\n" ); document.write( "and
\n" ); document.write( " $\"x%2B2=0\"$
\n" ); document.write( " $\"x=-2\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"y=%28-2%29%5E2-10=-6\"$
\n" ); document.write( "(-2,-6)
\n" ); document.write( "and
\n" ); document.write( " $\"x%2B3=0\"$
\n" ); document.write( " $\"x=-3\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"y=%28-3%29%5E2-10=-1\"$
\n" ); document.write( "(-3,-1)
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