What is the standard form of the equation of the parabola with a directrix at x=-3 and a focus at (6,2)?

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Answer 1 · 2017-12-31T11:56:57

The standard equation of horizontal parabola is
#(y-2)^2 = 18(x-1.5) #

Focus is at #(6,2) #and directrix is #x=-3#. Vertex is at midway

between focus and directrix. Therefore vertex is at

#((6-3)/2,2) or (1.5,2)#.Here the directrix is at left of

the vertex , so parabola opens right and #p# is positive.

The standard equation of horizontal parabola opening right is

#(y-k)^2 = 4p(x-h) ; h=1.5 ,k=2#

or #(y-2)^2 = 4p(x-1.5) # The distance between focus and

vertex is #p=6-1.5=4.5#. Thus the standard equation of

horizontal parabola is #(y-2)^2 = 4*4.5(x-1.5) # or

#(y-2)^2 = 18(x-1.5) #

graph{(y-2)^2=18(x-1.5) [-40, 40, -20, 20]}