Question 154307
one general form of the equation of a parabola is (x-h)^2=4p(y-k)
__ (the x and y may be switched, depending on the direction of the parabola)
__ the vertex is (h,k), and p is the distance from the vertex to the focus
__ since the vertex is midway between the focus and directrix, -p is the distance from the vertex to the directrix
__ the vertex and focus are on the axis of symmerty, the directrix is perpendicular to the axis


so, the "trick" is to manipulate the equation until it looks like the general form


x^2+6x+8y+1=0 __ subtracting 8y+1 __ x^2+6x=-8y-1 __ completing the square by adding (6/2)^2 (from 6x) __ x^2+6x+9=-8y-1+9


x^2+6x+9=-8y+8 __ factoring __ (x+3)^2=-8(y-1)
__ vertex is (-3,1)
__ focus is (-3,-1)
__ directrix is y=3



y^2-2y-8x+1=0 __ subtracting -8x+1 __ y^2-2y=8x-1 __ completing the square by adding (-2/2)^2 __ y^2-2y+1=8x-1+1


y^2-2x+1=8x __ factoring __ (y-1)^2=8(x-0)
__ vertex is (0,1)
__ focus is (2,1)
__ directrix is x=-2