document.write( "Question 975216: Write the equation of the parabola that has its focus at the point (4,7) and whose directrix is x=-2. \n" ); document.write( "

Algebra.Com's Answer #597024 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "The trouble with parabolas is that different books use different notation.\r\n" );
document.write( "They are all equivalent, but they are just different enough to cause confusion.\r\n" );
document.write( "I will arbitrarily pick one of the notations.  If your book is different, just\r\n" );
document.write( "tell me what your book gives for the standard equation for a parabola in the\r\n" );
document.write( "thank-you note below and I'll change it on here to fit your notation. One\r\n" );
document.write( "common one is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where (h,k) = the vertex, p is the distance from center to focus, positive\r\n" );
document.write( "if parabola opens right and negative if it opens left.\r\n" );
document.write( "\r\n" );
document.write( "We plot the focus point and draw the the directrix, a vertical line\r\n" );
document.write( "through x=-2 on the x-axis:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The vertex is a point exactly half-way between the focus and the directrix\r\n" );
document.write( "line. That is the point (h,k) = (1,7)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "p = the distance from the center to the focus is 3 units here.\r\n" );
document.write( "\r\n" );
document.write( "The focal chord (sometimes called the latus rectum) is a line which is 4p\r\n" );
document.write( "units long (in this case 4*3 or 12 units long) bisected at the focus.  So\r\n" );
document.write( "it's 6 units up from the focus and 6 units down from the focus:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "And now we can sketch the parabola:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "h=1,k=7, 4p = 12, so the equation is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );