What is the equation of the parabola with a focus at (0, 2) and vertex at (0,0)?

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Answer 1 · 2017-04-26T17:35:25

#y = 1/8x^2#

If the focus is above or below the vertex, then the vertex form of the equation of the parabola is:

#y = a(x-h)^2+k" [1]"#

If the focus is to the left or right the vertex, then the vertex form of the equation of the parabola is:

#x = a(y-k)^2+h" [2]"#

Our case uses equation [1] where we substitute 0 for both h and k:

#y = a(x-0)^2+0" [3]"#

The focal distance, f, from the vertex to the focus is:

#f = y_"focus"-y_"vertex"#

#f = 2-0#

#f = 2#

Compute the value of "a" using the following equation:

#a = 1/(4f)#

#a = 1/(4(2))#

#a = 1/8#

Substitute #a = 1/8# into equation [3]:

#y = 1/8(x-0)^2+0#

Simplify:

#y = 1/8x^2#