Question
Write the equation of the parabola in standard and general form whose vertex is at the origin and directrix of equation y = 3. Find the coordinate of the focus, length of the latus rectum (focal width), the x- and y-intercepts.
Answers
oobleck
recall that the parabola
x^2 = 4py
has
vertex at (0,0)
directrix is the line y = -p
so that means our parabola has p = -3, giving us
x^2 = -12y
focus is (0,p) = (0,-3)
latus rectum is 4|p| = 12
x^2 = 4py
has
vertex at (0,0)
directrix is the line y = -p
so that means our parabola has p = -3, giving us
x^2 = -12y
focus is (0,p) = (0,-3)
latus rectum is 4|p| = 12