document.write( "Question 614898: What is the focus of the conic section
\n" ); document.write( "12x + y^2 - 14y + 1=0 \n" ); document.write( "
Algebra.Com's Answer #386755 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
What is the focus of the conic section
\n" ); document.write( "12x + y^2 - 14y + 1=0
\n" ); document.write( "complete the square
\n" ); document.write( "(y^2-14y+49)=-12x-1+49
\n" ); document.write( "(y-7)^2=-12x+48
\n" ); document.write( "(y-7)^2=-12(x-4)
\n" ); document.write( "This is an equation of a parabola that opens leftwards.
\n" ); document.write( "Its standard form of equation: (y-k)^2=4p(x-h), (h,k)=(x,y) coordinates of the vertex
\n" ); document.write( "For given equation:(y-7)^2=-12(x-4)
\n" ); document.write( "vertex:(4,7)
\n" ); document.write( "axis of symmetry: y=7
\n" ); document.write( "4p=12
\n" ); document.write( "p=3
\n" ); document.write( "focus: (1,7) (p units to the left of vertex on the axis of symmetry)
\n" ); document.write( " \n" ); document.write( "
\n" );