Question

find the coordinates of the focus,vertex and equation of the directrix for y^2+8x+40=0

Answer 1

y^2+8x+40=0 => sideways parabola, opens to the left:
If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)^2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p
y^2 = -8(x + 5) => vertex at(-5 , 0)
4p = -8
p = -2
x = h - p = -5 + 2 = -3 => directrix