Graph of the parabola #2

Question

Find the focus, directrix, and equation of the parabola with vertex at the origin, axis along y-axis; opening upward; and the length of the latus rectum is 12. Sketch the graph.

Answer 1

v ertex = (0,0)

focus = (0,3), directrix is y=-3

axis of symmetry is x=0

2 other points on the parabola are (6,3) and (-6, 3)

y=ax^2

3 =36a

a = 3/36 = 1/13

y = (x^2)/13 is the parabola equation

or

13y = x^2

an upward opening parabola with vertex at the origin