document.write( "Question 1183792: Locate the vertex, the focus, and the ends of the latus rectum and find the equation of the directrix, then draw the parabola whose equation is (y-1)² = -8(x-2). \n" ); document.write( "
Algebra.Com's Answer #814263 by Edwin McCravy(20059)\"\" \"About 
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document.write( " (y-1)² = -8(x-2)\r\n" );
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document.write( "the -2 tells that the x-coordinate of the vertex is +2.\r\n" );
document.write( "the -1 tells that the y-coordinate of the vertex is +1.\r\n" );
document.write( "So the vertex is (1,2)\r\n" );
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document.write( "The fact that the sign before the 8 is negative tells us that the parabola\r\n" );
document.write( "opens leftward. \r\n" );
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document.write( "The fact that the x is in the expression that is not squared tells\r\n" );
document.write( "us the that its axis of symmetry is horizontal, and opens right or left.\r\n" );
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document.write( "The absolute value of the -8, or 8, tells us two things.\r\n" );
document.write( "1. 8 divided by 4, which is 2, is the distance between the vertex and the\r\n" );
document.write( "focus (2 is also the perpendicular distance from the vertex to the\r\n" );
document.write( "directrix). \r\n" );
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document.write( "So the focus is 2 units from the vertex, inside the parabola.\r\n" );
document.write( "So the focus is (0,1)\r\n" );
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document.write( "And the dirctrix is a vertical line 2 units from the vertex outside the\r\n" );
document.write( "parabola, so it is the vertical line whose equation is y = 4.\r\n" );
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document.write( "2. The latus rectum (vertical distance across the parabola at the focus) is 8 units long.\r\n" );
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document.write( "The ends of the latus rectum is 4 units up and down from the focus, which\r\n" );
document.write( "are (0,5) and (0,-3)\r\n" );
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document.write( "Edwin
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