document.write( "Question 1166898: Write the standard equation of the ellipse with the given properties
\n" ); document.write( " Horizontal major axis of length 10, center at the origin, and passes through ( 3,16/5 )
\n" ); document.write( " F_1 (-7,-3),F_2 ( -1,-3) and V_1 (1,-3)
\n" ); document.write( " C(0,0), a vertex is 8 units from a focus and 18 units from the other
\n" ); document.write( " F_1 (-4,0),F_2 ( 4,0) and passing through (4,1)
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Algebra.Com's Answer #791462 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing the first one for you, I'll do one EXACTLY like it \r\n" );
document.write( "step-by-step.  So I'll do this one instead:\r\n" );
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\n" ); document.write( " Write the standard equation of the ellipse with the given properties
\n" ); document.write( " Horizontal major axis of length 26, center at the origin, and passes
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document.write( "Since its center is (0,0) and has horizontal major axis of length 26, it\r\n" );
document.write( "extends half of 26, which is 13 to the left and 13 to the right, and\r\n" );
document.write( "has vertices at (-13,0) and (13,0).  So it looks like this and passes through\r\n" );
document.write( "(5, 60/13)\r\n" );
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document.write( "Since it is a horizontal ellipse, it has this equation:\r\n" );
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document.write( "\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\", \r\n" );
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document.write( "where \"a\" is the length of the semi-major axis, which is half of \r\n" );
document.write( "the major axis, which is 13, the center is (h,k)=(0,0), we have \r\n" );
document.write( "this much of the equation:\r\n" );
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document.write( "\"%28x-0%29%5E2%2F13%5E2%2B%28y-0%29%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "\"x%5E2%2F169%5E%22%22%2By%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "All we need is b2.  We can find \"b2\" because we know that the ellipse \r\n" );
document.write( "passes through (5, 60/13)\r\n" );
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document.write( "So we substitute 5 for x and 60/13 for y:\r\n" );
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document.write( "\"x%5E2%2F169%5E%22%22%2By%5E2%2Fb%5E2=1\"\r\n" );
document.write( "\"5%5E2%5E%22%22%2F169%5E%22%22%5E%22%22%2B%2860%2F13%29%5E2%2Fb%5E2=1\"\r\n" );
document.write( "\"25%5E%22%22%5E%22%22%2F169%5E%22%22%5E%22%22%2B%283600%2F169%29%2Fb%5E2=1\"\r\n" );
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document.write( "Multiply through by 169b2\r\n" );
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document.write( "\"25b%5E2%2B169%2Aexpr%283600%2F169%29=169b%5E2\"\r\n" );
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document.write( "\"25b%5E2%2Bcross%28169%29expr%283600%2Fcross%28169%29%29=169b%5E2\"\r\n" );
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document.write( "\"25b%5E2%2B3600=169b%5E2\"\r\n" );
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document.write( "\"3600=144b%5E2\"\r\n" );
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document.write( "\"25=b%5E2\"\r\n" );
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document.write( "So the equation is\r\n" );
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document.write( "\"x%5E2%2F169%5E%22%22%2By%5E2%2F25%5E%22%22=1\"\r\n" );
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document.write( "Now do your first one the exact same way step-by-step.\r\n" );
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document.write( "When I have time I'll do ones just like the other two.\r\n" );
document.write( "When I get time, I'll come back and do them.  I'll notify\r\n" );
document.write( "you when I do.\r\n" );
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document.write( "Edwin
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\n" ); document.write( "\n" ); document.write( "F_1 (-7,-3),F_2 ( -1,-3) and V_1 (1,-3)
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