document.write( "Question 105125: When solving systems of relations, how do you know which conic section you will have by looking at the equation. For example: x^2-y^2=9, x+y=5 \n" ); document.write( "
Algebra.Com's Answer #76492 by Fombitz(32388)\"\" \"About 
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In general, you can spot sonic sections by their equations, of the form,
\n" ); document.write( "Circle: \"%28x%29%5E2%2B%28y%29%5E2=R%5E2\"
\n" ); document.write( "Ellipse: \"%28x%2Fa%29%5E2%2B%28y%2Fb%29%5E2=1\"
\n" ); document.write( "Parabola: \"y=ax%5E2%2Bbx%2Bc\"
\n" ); document.write( "Hyperbola: \"%28x%2Fa%29%5E2-%28y%2Fb%29%5E2=1\"
\n" ); document.write( "Sometimes your equation will not look so neat and you'll have to do some manipulation to get it to look like these standard forms.
\n" ); document.write( "Your first example,
\n" ); document.write( "\"x%5E2-y%5E2=9\"
\n" ); document.write( "\"%28x%2F3%29%5E2-%28y%2F3%29%5E2=1\" is a hyperbola.
\n" ); document.write( "\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+sqrt%28x%5E2-9%29%2C-sqrt%28x%5E2-9%29%29+\"
\n" ); document.write( "Your second example,
\n" ); document.write( "\"x%2By=5\"
\n" ); document.write( "\"y=5-x\" is a linear equation, yielding a straight line, and is not a conic section.
\n" ); document.write( "It has a slope of -1 and a y-intercept of 5.
\n" ); document.write( "\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+5-x%29+\" \n" ); document.write( "
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