document.write( "Question 1194603: Find the center, vertices, foci, ends of the latera recta and the equations of the directrices of the ellipse whose equation is y^2/36 + x^2/25 =1 and sketch the graph. \n" ); document.write( "
Algebra.Com's Answer #826857 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"y%5E2%2F36%5E%22%22%2Bx%5E2%2F25%5E%22%22=1\"\r\n" );
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document.write( "Write as\r\n" );
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document.write( "\"%28y-0%29%5E2%2F6%5E2%2B%28x-0%29%5E2%2F5%5E2=1\"\r\n" );
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document.write( "Compare to \r\n" );
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document.write( "\"%28y-k%29%5E2%2Fa%5E2%2B%28x-h%29%5E2%2Fb%5E2=1\" which is an ellipse taller than it is wide\r\n" );
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document.write( "h=0, k=0, a=6, b=5 (a is larger than b in an ellipse)\r\n" );
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document.write( "From the center (h,k) = (0,0), go a=6 units up and down, to form\r\n" );
document.write( "the major axis, and go b=5 units right and left, to form the minor axis.\r\n" );
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document.write( "The vertices are (h,k±a) = (0,a) and (0,-6)\r\n" );
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document.write( "The co-vertices are (h±a,k) = (-5,0) and (0,-5)\r\n" );
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document.write( "The major and minor axes are in green below:\r\n" );
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document.write( "We sketch in the ellipse:\r\n" );
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document.write( "We calculate c, the distance from Center to foCus.\r\n" );
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document.write( "\"c%5E2=a%5E2-b%5E2\"\r\n" );
document.write( "\"c%5E2=6%5E2-5%5E2\"\r\n" );
document.write( "\"c%5E2=36-25\"\r\n" );
document.write( "\"c%5E2=11\"\r\n" );
document.write( "\"c=sqrt%2811%29\"\r\n" );
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document.write( "So the foci are (h,k±c) = \"%28matrix%281%2C3%2C0%2C%22%2C%22%2Csqrt%2811%29%29%29\" and \"%28matrix%281%2C3%2C0%2C%22%2C%22%2C-sqrt%2811%29%29%29\"\r\n" );
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document.write( "Draw the chords through them (in blue), which are \r\n" );
document.write( "the latus recta:\r\n" );
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document.write( "We find the ends of the latus recta by substituting y=±√11 for y\r\n" );
document.write( "in the equation of the ellipse and solving for x\r\n" );
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document.write( "\"%28%22%22+%2B-+sqrt%2811%29%29%5E2%2F36%5E%22%22%2Bx%5E2%2F25%5E%22%22=1\"\r\n" );
document.write( "\"11%5E%22%22%2F36%5E%22%22%2Bx%5E2%2F25%5E%22%22=1\"\r\n" );
document.write( "\"x%5E2%2F25%5E%22%22=1-11%5E%22%22%2F36%5E%22%22\"\r\n" );
document.write( "\"x%5E2%2F25%5E%22%22=25%5E%22%22%2F36%5E%22%22\"\r\n" );
document.write( "\"x%5E2=25%5E2%2F36%5E%22%22\"\r\n" );
document.write( "\"x=%22%22+%2B-+5%2F6\"\r\n" );
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document.write( "So the ends of the latus recta are \r\n" );
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document.write( "\"%28matrix%281%2C3%2C5%2F6%2C%22%2C%22%2Csqrt%2811%29%29%29\",\"%28matrix%281%2C3%2C5%2F6%2C%22%2C%22%2C-sqrt%2811%29%29%29\",\r\n" );
document.write( "\"%28matrix%281%2C3%2C-5%2F6%2C%22%2C%22%2Csqrt%2811%29%29%29\",\"%28matrix%281%2C3%2C-5%2F6%2C%22%2C%22%2C-sqrt%2811%29%29%29\"\r\n" );
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document.write( "Edwin
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