What is the standard form of the equation of the parabola with a directrix at x=4 and a focus at (-7,-5)?

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Answer 1 · 2017-12-25T12:22:18

The standard equation of parabola is #(y+5.5)^2 = -22(x+1.5) #

Focus is at #(-7,-5) # and directrix is #x=4#. Vertex is at midway

between focus and directrix. Therefore vertex is at

#((-7+4)/2,-5) or (-1.5,-5)# The equation of horizontal

parabola opening left is

#(y-k)^2 = -4p(x-h) ; h=-1.5 ,k=-5#

or #(y+5.5)^2 = -4p(x+1.5) # . The distance between focus and

vertex is #p=7-1.5=5.5#. Thus the standard equation of

horizontal parabola is #(y+5.5)^2 = -4*5.5(x+1.5) # or

#(y+5.5)^2 = -22(x+1.5) #

graph{(y+5.5)^2=-22(x+1.5) [-160, 160, -80, 80]}