How do you write an equation of a parabola with its vertex at the origin and focus at (0,3)?

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Answer 1 · 2017-09-06T11:53:43

The equation of parabola is # y= 1/12 x^2#

The standard vertex form of equation of parabola is

# y =a(x-h)^2+k ; (h,k)#being vertex , here #h=0 , k=0 #

The equation of parabola is # y =a(x-0)^2+0 or y =a x^2#

The focus is at #(0,3) # i.e above the vertex , so parabola

opens upward and #a# is positive. We know vertex is at

midway between focus and directrix , which is below the vertex.

The distance of directrix from vertex is #D=3 and D= 1/(4|a|#

#:. a = 1/(4*3) =1/12 # , So equation of parabola is # y =a x^2 # or

# y= 1/12 x^2#

graph{1/12 x^2 [-10, 10, -5, 5]} [Ans]