What is the the equation of a parabola whose focus is (-5,-5) and the directrix is x=-1?

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Answer 1 · 2018-04-06T12:56:36

The equation of parabola is #(y+5)^2 = -8(x+3)#

Focus is at #(-5,-5) #and directrix is #x=-1#. Vertex is at

midway between focus and directrix. Therefore vertex is at

#((-5-1)/2,-5) or (-3,-5)# The equation of horizontal

parabola opening left is

#(y-k)^2 = -4p(x-h) ; h=-3 ,k=-5#

or #(y+5)^2 = -4p(x+3) # . the distance between focus and

vertex is #p=|-5+3|=2#. Thus the equation of horizontal

parabola opening left is #(y+5)^2 = -4*2(x+3) # or

#(y+5)^2 = -8(x+3)#

graph{(y+5)^2=-8(x+3) [-40, 40, -20, 20]} [Ans]