document.write( "Question 249588: x^2/a^2+y^2/a^2-(2xy/a^2)cos45=sin^2(45)\r
\n" ); document.write( "\n" ); document.write( "please tell me what is the graphical shape of this equation. \n" ); document.write( "
Algebra.Com's Answer #181759 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The general equation of a conic section is:\r\n" );
document.write( "\r\n" );
document.write( "\"Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0\"\r\n" );
document.write( "\r\n" );
document.write( "The discriminant \"B%5E2-4AC\" is used to determine which \r\n" );
document.write( "conic section will result. \r\n" );
document.write( "\r\n" );
document.write( "1. If the discriminant is less than zero we have \r\n" );
document.write( "   (a). a circle if B = 0 and A = C, or \r\n" );
document.write( "   (b). an ellipse otherwise.\r\n" );
document.write( "2. If the discriminant is equal to zero we have a parabola.\r\n" );
document.write( "3. If the discriminant is greater than zero we have a hyperbola.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Your equation is:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2Fa%5E2%2By%5E2%2Fa%5E2-%282xy%2Fa%5E2%29Cos%28%2245%B0%22%29=Sin%5E2%28%2245%B0%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "We put the term in \"xy\" in between the terms in \"x%5E2%29%0D%0Aand+%7B%7B%7By%5E2\", and get 0 on the right, so it will be in \r\n" );
document.write( "the same form as above:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "we have  \r\n" );
document.write( "\r\n" );
document.write( "\"A=1%2Fa%5E2\",\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"C+=+1%2Fa%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"D=0\",  \"E=0\",  \"F=-Sin%5E2%28%2245%B0%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "So the discriminant = \r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( "Since the discriminant is negative, by the rules at the\r\n" );
document.write( "top we can conclude the equation represents an ellipse.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );