document.write( "Question 1016129: state the position of each lie with respect to the ellipse x^2/9 + y^2/36 = 1
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\n" ); document.write( "c.)2x+5y+3=0\r
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Algebra.Com's Answer #632575 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "state the position of each lie with respect to the ellipse x^2/9 + y^2/36 = 1
\n" ); document.write( "a.)y=2x+2
\n" ); document.write( "b.)y=-2x-9
\n" ); document.write( "c.)2x+5y+3=0\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "its differenet from the first one that i already asked. im not really good at math please help. and thank you again in advance
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document.write( "The way to solve this problem is as follows:\r\n" );
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document.write( "1. Express y via x from the given linear equation.\r\n" );
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document.write( "   (In your case it is just done in a.) and b.) ).\r\n" );
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document.write( "2. Substitute this expression into the equation for ellipse.\r\n" );
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document.write( "   You will get a quadratic equation.\r\n" );
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document.write( "3. If this quadratic equation has two real roots, then the straight line intersects the ellipse in two points.\r\n" );
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document.write( "   If this quadratic equation has one real root, then the straight line is tangent to the ellipse. \r\n" );
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document.write( "   If this quadratic equation has no real roots, then the straight line has no common points with the ellipse. \r\n" );
document.write( "   I.e. the straight line is outside the ellipse.\r\n" );
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document.write( "4. Therefore, when you got the quadratic equation, calculate and check its discriminant.\r\n" );
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document.write( "   If the discriminant is positive, then the quadratic equation has two real roots. \r\n" );
document.write( "   Hence, the straight line intersects the ellipse in two points.\r\n" );
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document.write( "   If the discriminant is zero, then the quadratic equation has one real root. \r\n" );
document.write( "   Hence, the straight line is tangent to the ellipse. \r\n" );
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document.write( "   If the discriminant is negative, then the quadratic equation has no real roots. \r\n" );
document.write( "   Hence, the straight line has no common points with the ellipse. I.e. the straight line is outside the ellipse.\r\n" );
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