Help On This One Please (:

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

f(x) = −one fourth x2

f(x) = one fourth x2

f(x) = −4x2

f(x) = 4x2

Question

Help On This One Please (:

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

f(x) = −one fourth x2

f(x) = one fourth x2

f(x) = −4x2

f(x) = 4x2

anonymous · Answer

@johnweldon1993 any idea how to do this lol :/ sorry im bugging

johnweldon1993 · Answer

Sure! And dont worry about bugging me :)

"focus of the parabola at (0, 1) 
directrix = -1

The focus lies above the directrix, so the parabola opens upwards. ...and we know that the equation of an UP parabola is 

y = a(x - h)² + k 


The vertex is halfway between focus and directrix so 
vertex (0, 1) 
h = 0
k = 1 

p = distance between focus and vertex = 2 
a = 1/(4p) = 1/4 

The equation of the parabola: 
y = (1/4)(x^2) + 1
y = (1/4)x^2

So  it would be the one forth x^2