document.write( "Question 1067045: The focus at (-2,-1) and the latus rectum joins the points (-2,2) and (-2,-4).find the equation of the parabola. \n" ); document.write( "
Algebra.Com's Answer #682502 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "There are 2 answers, because the parabola can open right or\r\n" );
document.write( "it can open left.\r\n" );
document.write( "\r\n" );
document.write( "            \r\n" );
document.write( "\r\n" );
document.write( "The equation of a parabola that faces left or right is\r\n" );
document.write( "\r\n" );
document.write( "\"%28y-k%29%5E2\"\"%22%22=%22%22\"\"4p%28x-h%29\"\r\n" );
document.write( "\r\n" );
document.write( "Where (h,k) is the vertex\r\n" );
document.write( "\r\n" );
document.write( "If p is taken positive it opens to the right, if\r\n" );
document.write( "p is taken negative, it opens to the left.\r\n" );
document.write( "\r\n" );
document.write( "The latus rectum is 4p.  That's the green line, which\r\n" );
document.write( "is 6 units in length. I'll just do the one that opens\r\n" );
document.write( "to the right.  So 4p = +6, taking it positive.\r\n" );
document.write( "                   p = \"3%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "The distance p is the distance from the vertex to the \r\n" );
document.write( "focus.  So the vertex of the first parabola is \"3%2F2\"\r\n" );
document.write( "or \"1%261%2F2\" units left of the focus (-2,-1), and\r\n" );
document.write( "that point is\r\n" );
document.write( "\r\n" );
document.write( "(h,k) = \"%28matrix%281%2C3%2C-7%2F2%2C%22%2C%22%2C-1%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "So the equation of the first parabola above is\r\n" );
document.write( "\r\n" );
document.write( "\"%28y-%28-1%29%5E%22%22%29%5E2\"\"%22%22=%22%22\"\"6%28x-%28-7%2F2%29%5E%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28y%2B1%5E%22%22%29%5E2\"\"%22%22=%22%22\"\"6%28x%2B7%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "You can simplify that if your teacher wants you to.\r\n" );
document.write( "\r\n" );
document.write( "Now you find the equation of the parabola that opens to\r\n" );
document.write( "the left.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );