Find an equation of the parabola that has a focus at (2,13) vertex (2,7)

Question

Find an equation of the parabola that has a focus at (2,13) vertex (2,7)

y=

Find an equation directix:

y=

Answer 1

F(2,13) V(2,7)

It's horizontal parabola, upward opening

of the form y=a(x-2)^2 + 7 You need another point on the parabola to solve for a

draw a horizontal line from the focus to the parabola, it's distance is the same as from the focus to the directrix =2(6) = 12 the point on the parabola is (14,13)

directrix is the same distance to the vertex as the focus is to the vertex = 13-7 = 6

so the directrix is y=7-6 = 1 y=1

plug (14,13) into y=a(x-2)^2 + 7 to solve for a

13 =a(14-2)^2 +7 = 144a +7

144a =6

a = 1/24

y = (1/24)(x-2)^2 + 7 is the equation with the given vertex and focus