Question

Please help! 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.

Answer 1

To solve the equation of the parabola, I need to use the distance formula and substitute the focal point in (x1-y1). Also, I will use the distance formula for the direct x. Since it is a straight line, the x part could be eliminated and the remaining part of the formula would be used, substituting the y for the given measurement of the direct x. The two unfinished formulas would be combined and then solved for the equation. f(x) would be the unit of measurement for the parabola.

Answer 2

draw a perpendicular line from the directrix passing through the focus, this will be the line of symmetry. The vertex(h, k) will be located on the line half way between the focus and directrix. The distance from the focus to the vertex is called the focal length, call it a. The then equation is (x - h)^2 = 4a(y - k) the equation can be manipulated to y = 1/4a(x - h)^2 + k hope it helps