Question

Find the equation of the parabola given the focus (1,4) directrix y=1 ans sketch the graph

Answer 1

Ok, so for parabola a(x-h)^2 +k
abs(a) = 1/(4c) where c is the distance between the focus and directrix.

The distance is 4-1, or 3 (y coord of the focus - y coord of directrix)
so a = 1/(4*3) or 1/12
and the vertex (h,k) is the midpoint of the segment between the focus and directrix, which is (1, 2.5)

the parabola is 1/12*(x-1)^2 + 2.5