document.write( "Question 194051: What shape does this equation make? (circle, ellipse, hyperbola)
\n" ); document.write( "4x^2 + 16x + y^2 - 6y = -21 \n" ); document.write( "

Algebra.Com's Answer #145650 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Both the

and

term coefficients have the same sign, so it is either a circle or an ellipse. But the coefficients on the

and

terms are unequal, so it is an ellipse.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In summary:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Equal coefficients on

and

means circle.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Unequal coefficients, but the same sign means ellipse.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Opposite signs on the coefficients means hyperbola.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Zero coefficient on either the

and

terms (but NOT both) means parabola.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );