Question

What is the equation of a parabola with (−1, −3) as its focus and y = 1 as its directrix?

Answer 1

Based on the given focus (-1,-3) and directrix, y=1, it can be said that the parabola is opening downward since the equation of the directrix is a horizontal line, the latus rectum where the focus lies should be parallel to the directrix. By plotting the parabola, vertex can be drawn at point (-1,-1). Take note that the distance between focus and the vertex is equal to the distance from the vertex to the directrix, in this case this distance = 2. With this information known and by applying the standard equation for parabola opening downward, (x-h)^2 = -4a(y-k), or by substitution,
(x+1)^2 = -8(y+1) is the equation of the parabola.