document.write( "Question 120480: Please hepl solve this problem, vertex (2, 1), ends of the latus rectum (-1, -5) and (-1,7).\r
\n" ); document.write( "\n" ); document.write( "(y-k)^2= -4c(x-h)\r
\n" ); document.write( "\n" ); document.write( "(y- 1)^2= -4*3(x- 2)\r
\n" ); document.write( "\n" ); document.write( "y^2-2y+1= 12(x-2) \n" ); document.write( "
Algebra.Com's Answer #88332 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Please help solve this problem, vertex (2, 1),
\n" ); document.write( "ends of the latus rectum
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\n" ); document.write( "(y-k)^2= -4c(x-h)
\n" ); document.write( "(y-1)^2= -4*3(x-2)
\n" ); document.write( "y^2-2y+1= 12(x-2)
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document.write( "Plot the vertex and the ends of the latus rectum:\r\n" );
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document.write( "Draw the latus rectum:\r\n" );
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document.write( "Sketch the parabola with that vertex and which goes through\r\n" );
document.write( "the ends of the latus rectum:\r\n" );
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document.write( "The focus of the parabola is the midpoint of the latus\r\n" );
document.write( "rectum, which is (-1,1), so we may as well plot the focus, too.\r\n" );
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document.write( "Now we know that a parabola that opens to the right \r\n" );
document.write( "or left has the equation:\r\n" );
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document.write( "(y - k)² = 4c(x - h)\r\n" );
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document.write( "where the vertex is (h,k)\r\n" );
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document.write( "We also know that\r\n" );
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document.write( "c = the directed distance from the vertex to the focus.\r\n" );
document.write( "That means if we must move to the right to go from the \r\n" );
document.write( "vertex to the focus, then c is positive, and if we must\r\n" );
document.write( "move to the left, then c is negative. \r\n" );
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document.write( "the focus is the midpoint of the latus rectum. \r\n" );
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document.write( "The length of the latus rectum is |4c|.\r\n" );
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document.write( "Now our graph tells us that c is negative because we\r\n" );
document.write( "must go left to go from the vertex to the focus.\r\n" );
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document.write( "It also tells us that the length of the latus rectum\r\n" );
document.write( "is 12 by simply counting the units.\r\n" );
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document.write( "We know that c = -3 for two reasons. One reason is\r\n" );
document.write( "that it is the directed distance from the vertex to\r\n" );
document.write( "the focus, and that is 3 units going to the left, so\r\n" );
document.write( "c = -3.  The other reason is that the distance from\r\n" );
document.write( "the vertex to the focus in absolute value is 1/4 of\r\n" );
document.write( "the length of the latus rectum, or 1/4 of 12.\r\n" );
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document.write( "We are given that the vertex is (h,k) = (2,1).  So\r\n" );
document.write( "we substitute that into\r\n" );
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document.write( "(y - k)² = 4c(x - h)\r\n" );
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document.write( "and get\r\n" );
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document.write( "(y - 1)² = 4(-3)(x - 2)\r\n" );
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document.write( "(y - 1)² = -12(x - 2)\r\n" );
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document.write( "This is the same as the second choice above.\r\n" );
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document.write( "Edwin
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