Question

Write an equation of the parabola that has a focus at (0,0 and a directrix at y=4 ?

I don't understand the question ?

Answer 1

`y=-1/8x^2+2`

Explanation:

Parabola is the locus of a point which moves so that its distance from a given point called focus and a line called directrix is always equal.

Let the point be `(x,y)`. Here the focus is at `(0,0)` and its distance from focus is `sqrt(x^2+y^2)`

and its distance from directrix `y=4` is `|y-4|`

and equation of parabola is

`sqrt(x^2+y^2)=|y-4|` and squaring it we get

`x^2+y^2=y^2-8y+16`

or `-8y=x^2-16`

or `y=-1/8x^2+2`

graph{(y+1/8x^2-2)(y-4)(x^2+y^2-0.03)=0 [-10, 10, -5, 5]}