Find the equation of the parabola determined by the given information.
Focus (3,5), directrix x = -1
Notice that the directrix is a vertical line. Since the axis of symmetry is perpendicular to the directrix, then it is a horizontal line.
The parabola with a horizontal axis of symmetry will have directrix x = h –p,
focus (h + p,k), and standard equation = 4p(x – h).
Since the directrix of the parabola is x = -1, then -1, then -1 = h – p.
Since the x-value of the focus is 3, then 3 = h + p.
Find h and p using any method for solving a system of equation. Using the elimination method, eliminate p and solve for h.
h = 1
substitute the value for h into one of the equation to solve for p.
p = 2
k is the y – value for h , p, and k into standard equation of a parabola.
= 4*2(x – 1)
= 8(x – 1)