document.write( "Question 1186882: center at the origin; a focus (0,2); vertex at (0,3) \n" ); document.write( "

Algebra.Com's Answer #817850 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "center at the origin; a focus (0,2); vertex at (0,3)
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document.write( "The focus is closer to the center than the vertex ---> hence, the conic section is an ellipse.\r\n" );
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document.write( "A focus and a vertex lie on vertical line x= 0  ---> hence, the major axis is vertical.\r\n" );
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document.write( "The length of the major semi-axis is a = 3.\r\n" );
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document.write( "We find the length of the minor semi-axis b from the equation\r\n" );
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document.write( "    b = ,  where c is the eccentriciry  c= 2 (given).\r\n" );
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document.write( "So,  b =  =  = .\r\n" );
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document.write( "Thus the equation of the ellipse is\r\n" );
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document.write( "     +  = 1.\r\n" );
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