Question

Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.

Answer 1

you know what this looks like? if so we can find the equation easily (no one likes these conic sections problems, but they are not that hard)

Answer 2

i have no idea how it looks, that's all I was given

Answer 3

\(y=-1\) is a horizontal line, and \((0,1)\) is a point on the y axis

Answer 4

the vertex of your parabola is half way between the directrix and the focus, so it is at \((0,0)\) the origin

Answer 5

since it opens up, the \(x\) term is squared
and since the vertex is \((0,0)\) it looks like
\[4py=x^2\] all you need is \(p\)

Answer 6

p is the distance between the focus and the vertex
the distance between \((0,0)\) and \((0,1)\) is 1, making your equation
\[4y=x^2\]

Answer 7

so its a positive 4
would it be 4x^2?