Question

What is the equation of the parabola with the given directrix and focus.

Directrix: y = -3; Focus: (-2, 1)

Answer 1

well have you plotted the information so you know the type of parabola you are looking at..?

Answer 2

I don't know how. :D

Answer 3

Any point on the parabola (x,y) is at equal distance from the directrix and the focus.

What is the distance of a point (x,y) on the parabola from the focus (-2,1)?
What is the distance of the point (x,y) from the directrix y = -3?

Equate the two distances and simplify and you will have the equation of the parabola.

Answer 4

well because the directrix is below the focus
its in the form

\[(x - h)^2 = 4a(y - k)\]

Answer 5

I don't understand

Answer 6

ok... well look at the picture the perpendicular distance from the focus to the directrix is 2a....



so whats the value of 2a....?