What is the equation of the parabola with a focus at (2,15) and a directrix of y= -25?

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Answer 1 · 2017-10-23T10:52:26

The equation of parabola is #y=1/20(x-2)^2-5 #

Focus is at #(2,15) #and directrix is #y=-25#. Vertex is at midway

between focus and directrix. Therefore vertex is at #(2,(15-25)/2)#

or at #(2, -5)# . The vertex form of equation of parabola is

#y=a(x-h)^2+k ; (h.k) ;# being vertex. # h=2 and k = -5#

So the equation of parabola is #y=a(x-2)^2-5 #. Distance of

vertex from directrix is #d= 25-5=20#, we know # d = 1/(4|a|)#

#:. 20 = 1/(4|a|) or |a|= 1/(20*4)=1/80#. Here the directrix is behind

the vertex , so parabola opens upward and #a# is positive.

#:. a=1/80# . The equation of parabola is #y=1/20(x-2)^2-5 #

graph{1/20(x-2)^2-5 [-40, 40, -20, 20]} [Ans]