An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
so the focus is on the opening side of the parabola
so for a vertex of (h,k) opening up and down (x-h)²=4p(y-k) p is the distance from vertex to focus it is also the distance from the vertex to the closes point on directix 2p=distance from focus to directix
p is positive if the focus is above the directix
ok y=9 and (7,6) 9>6 directix is above the vertex p is negative find distance from 9 to 6 is 3 3=2p 1.5=p p is negative and the vertex will be 1.5 above the focus and 1.5 below the directix vertex is (7,7.5)
