Question

Determine the focus and directrix of the given parabola, and sketch the graph: x^2 = -4y

Answer 1

bring the equation to the standard form and get the directrix and focus using their formulae

Answer 2

it is (0,0) and y = 0

Answer 3

x^2 = -4y (1)

First rearrange the equation into the standard form y=something

y=(x^2) (2)
----
(-4)

Now using (3) the standard derivation from the distance formula

y=x^2 (3)
---
4(p)

substitute the values from (2) so that 4xp = -4

y=x^2
---
4(-1)

so 4p = -4: with p=-1

p=-1

Directrix is -p so -(-1) is 1

so curve points downwards symetrical at 0 and focus is -1