document.write( "Question 833535: hello
\n" ); document.write( "am stuck in a question which is
\n" ); document.write( "find the equation of ellipse which the focus is (2.3) and the directrix equation is x+y+1=0? \n" ); document.write( "
Algebra.Com's Answer #502818 by Edwin McCravy(20060) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "That's not enough information. You must be given something else,\r\n" );
document.write( "because there are infinitely many ellipses with different \r\n" );
document.write( "eccentricities 0 < e < 1 that have the same focus and directrix.\r\n" );
document.write( "So you must be given something else besides what you posted.  \r\n" );
document.write( "There must be a way to determine the eccentricity, so that we \r\n" );
document.write( "can set the ratio of the distance from an arbitrary point(x,y) \r\n" );
document.write( "to the focus and directrix equal to that eccentricity.  We \r\n" );
document.write( "either have to be given the center, the other focus, a vertex \r\n" );
document.write( "or some point that the graph passes through.\r\n" );
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document.write( "I'm going to suppose that you were given that the ellipse passes \r\n" );
document.write( "through the point P(,).  I picked that point\r\n" );
document.write( "just because it works out fairly easier than some of the others.\r\n" );
document.write( "You may be given some other information but I'll assume you were\r\n" );
document.write( "given this point.  If you were given a vertex, that will do, and\r\n" );
document.write( "would actually be easier.\r\n" );
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document.write( "We can find the eccentricity by getting the ratio of the lengths of\r\n" );
document.write( "those two green lines. First we find the distance \r\n" );
document.write( "from that supposedly given point P(,) to the focus \r\n" );
document.write( "by the distance formula:\r\n" );
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document.write( "Then we find the distance from P(,) to the directrix \r\n" );
document.write( "using the formula:\r\n" );
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document.write( "Perpendicular distance from the point (x₁,y₁)\r\n" );
document.write( "to the line Ax+By+C=0 is\r\n" );
document.write( "d = \r\n" );
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document.write( "where the line is x+y+1=0 and the point is \r\n" );
document.write( "(x₁,y₁) = P(,), and\r\n" );
document.write( "A=1, B=1, C=1\r\n" );
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document.write( "d = \r\n" );
document.write( "d = \r\n" );
document.write( "d = \r\n" );
document.write( "d = \r\n" );
document.write( "d = \r\n" );
document.write( "d = \r\n" );
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document.write( "d = 5√2\r\n" );
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document.write( "So the eccentricity is \r\n" );
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document.write( "So the eccentricity is ,  so we can go from there.\r\n" );
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document.write( "We let (x,y) be an arbitrary point on the graph:\r\n" );
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document.write( "Now we will do the same thing with this arbitrary point (x,y) as we did \r\n" );
document.write( "with the point P(,) that I assumed that you were \r\n" );
document.write( "given.  \r\n" );
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document.write( "We find the distance from the arbitrary point (x,y) to the focus \r\n" );
document.write( "by the distance formula:\r\n" );
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document.write( "Then we find the distance from the arbitratrary point (x,y) to the \r\n" );
document.write( "directrix using the same formula:\r\n" );
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document.write( "Perpendicular distance from the point (x₁,y₁)\r\n" );
document.write( "to the line Ax+By+C=0 is\r\n" );
document.write( "d = \r\n" );
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document.write( "where the line is x+y+1=0 and this time the arbitrary point is \r\n" );
document.write( "(x₁,y₁) = (x,y), and the same\r\n" );
document.write( "A=1, B=1, C=1\r\n" );
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document.write( "d = \r\n" );
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document.write( "Then the ratio of the two distances equals the eccentricity \r\n" );
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document.write( "Multiply both sides by \r\n" );
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document.write( "Multiply both sides by \r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "That simplifies to the equation:\r\n" );
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document.write( "Whatever the missing information was, the solution will be\r\n" );
document.write( "similar to the above.\r\n" );
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document.write( "Edwin
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