Algebra.Com's Answer #433414 by AnlytcPhil(1807)![\"\"](\"/images/stars/stars-12.gif\")  
You can put this solution on YOUR website!
Find the equation in standard form of the given parabola as a conic section. Focus is at (-2, 5) Directrix is y=1.
\n" );
document.write( "\r\n" );
document.write( "That will either be \r\n" );
document.write( "\r\n" );
document.write( "(x-h)² = 4p(y-k), if the parabola is like a U or an upside down U.\r\n" );
document.write( "\r\n" );
document.write( "or it will be\r\n" );
document.write( "\r\n" );
document.write( "(y-k)² = 4p(x-h), if the parabola is like a C or a backwards C.\r\n" );
document.write( "\r\n" );
document.write( "where (h,k) is the vertex and p is the distance from the vertex\r\n" );
document.write( "to the focus and also the distance from the vertex to the\r\n" );
document.write( "directrix. p is taken positive is like a U or a C, and negative\r\n" );
document.write( "if it is like an upside-down U or a backwards C.\r\n" );
document.write( "\r\n" );
document.write( "First we will sketch the graph:\r\n" );
document.write( "\r\n" );
document.write( "Plot the focus and graph the directrix:\r\n" );
document.write( "\r\n" );
document.write( "   \r\n" );
document.write( "\r\n" );
document.write( "Draw a line from the focus straight down through the vertex\r\n" );
document.write( "all the way to the directrix: \r\n" );
document.write( "\r\n" );
document.write( "   \r\n" );
document.write( "\r\n" );
document.write( "Now sketchin the parabola through the vertex and the upper\r\n" );
document.write( "outer corners of those two squares, like this:\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "So the parabola is like a U so it has the form:\r\n" );
document.write( "\r\n" );
document.write( "(x-h)² = 4p(y-k) and p is taken positive.\r\n" );
document.write( "\r\n" );
document.write( "The vertex is V(h,k) = V(-2,3) and p is the distance from the vertex to\r\n" );
document.write( "the focus and also the distance from the vertex to the\r\n" );
document.write( "directrix which is p=2, so substitute h=-2,k=3,p=2:\r\n" );
document.write( "\r\n" );
document.write( "(x-(-2))² = 4(2)(y-3)\r\n" );
document.write( "\r\n" );
document.write( "(x+2)² = 8(y-3)\r\n" );
document.write( "\r\n" );
document.write( "Edwin \n" );
document.write( " |