document.write( "Question 972212: center at (4,6); focus at (9,6); contains the point (4,7)
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Algebra.Com's Answer #594605 by Edwin McCravy(20060)\"\" \"About 
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center at (4,6); focus at (9,6); contains the point (4,7)
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document.write( "If it's an ellipse that looks like this \"drawing%2820%2C10%2C-2%2C2%2C-1%2C1%2Carc%280%2C0%2C-3.9%2C1.9%29+%29\", its equation is\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( "If it's an ellipse that looks like this \"drawing%2810%2C20%2C-1%2C1%2C-2%2C2%2Carc%280%2C0%2C1.9%2C-3.9%29+%29\", its equation is\r\n" );
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document.write( "\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"\r\n" );
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document.write( "We plot the three given points, and connect the center to the given\r\n" );
document.write( "focus in red, for that is the value of \"c\". Since the given point \r\n" );
document.write( "(4,7) on the ellipse has the same x-coordinate as the center, that\r\n" );
document.write( "point has to be the covertex, so we connect the center to it also,\r\n" );
document.write( "in green, for that is the value of \"b\", the semi-minor axis. \r\n" );
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document.write( "We see that the ellipse has the 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( "And that the center (h,k) = (4,6), and c = 5 because the red line is\r\n" );
document.write( "5 units long.  The other focus has to be 5 units to the left of the \r\n" );
document.write( "center, which is (-1,6).  We can calculate the value of \"a\", by using \r\n" );
document.write( "the relationship between a,b, and c for ellipses: \r\n" );
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document.write( "\"c%5E2=a%5E2-b%5E2\"\r\n" );
document.write( "\"5%5E2=a%5E2-1%5E2\"\r\n" );
document.write( " \"25=a%5E2-1\" \r\n" );
document.write( " \"26=a%5E2\"\r\n" );
document.write( "\"sqrt%2826%29=a\"\r\n" );
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document.write( "That's about 5.1. So it's equation is\r\n" );
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document.write( "\"%28x-4%29%5E2%2F26%2B%28y-6%29%5E2%2F1=1\"\r\n" );
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document.write( "we sketch in the ellipse:\r\n" );
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document.write( "Edwin
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