document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581360>Question 581360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the focus of this parabola?\r<BR>\n" );
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document.write( "X^2 + 12X - 24Y + 84 = 0 </SPAN>\n" );
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document.write( "X^2 + 12X - 24Y + 84 = 0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "(x^2+12x+36)-24y+84-36=0<BR>\n" );
document.write( "(x+6)^2-24y+48=0<BR>\n" );
document.write( "(x+6)^2=24y-48<BR>\n" );
document.write( "(x+6)^2=24(y-2)<BR>\n" );
document.write( "This is an equation of a parabola which opens upwards of the standard form: (x-h)^2=4p(y-k), (h<k) being the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "vertex: (-6,2)<BR>\n" );
document.write( "axis of symmetry: x=-6<BR>\n" );
document.write( "4p=24<BR>\n" );
document.write( "p=6<BR>\n" );
document.write( "x-coordinate of focus=-6 <BR>\n" );
document.write( "y-coordinate of focus=8 (p units above the vertex on the axis of symmetry)<BR>\n" );
document.write( "focus: (-6,8)<BR>\n" );
document.write( " </SPAN>\n" );
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