What is the standard form of the equation of the parabola with a directrix at x=3 and a focus at (-5,-5)?

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Answer 1 · 2018-06-02T11:27:40

The equation of parabola is #(y+5)^2 = -16(x+1)#

Focus is at #(-5,-5) #and directrix is #x=3#. Vertex is at midway

between focus and directrix. Therefore vertex is at

#((-5+3)/2,-5) or (-1,-5)# The directrix is at the right side

of vertex ,so, the horizontal parabola opens left. The equation of

horizontal parabola opening left is #(y-k)^2 = -4 p(x-h)#

# h=-1 ,k=-5# or #(y+5)^2 = -4 p(x+1) # . the distance

between focus and vertex is #p=5-1=4#. Thus the standard

equation of horizontal parabola is #(y+5)^2 = -4*4(x+1) #

or #(y+5)^2 = -16(x+1)#

graph{(y+5)^2= -16(x+1) [-80, 80, -40, 40]} [Ans]