Write the equation given the vertex is (-1,4) and the directrix line is x=1. help please?

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Answer 1 · 2018-05-10T12:35:55

The equation of parabola is # y^2 +8 x -8 y +24=0#

The vertex is at # (-1,4)# , directrix is #x=1#

Distance of vertex from directrix is #a=1- (-1)=2#,

Vertex is at midway between focus and directrix.

Therefore focus is at # (-3,4)# . Directrix is at right

of vertex , so parabola open left. The equation of horizontal

parabola opening left is

#(y-k)^2 = -4 a (x-h) ; h=-1 ,k=4#

#(y-4)^2 = -4 *2 (x +1) or (y-4)^2 = -8(x +1)# or

#y^2 - 8 y+16+8 x+8=0 or y^2 +8 x -8 y +24=0#

The equation of parabola is # y^2 +8 x -8 y +24=0#

graph{y^2+8 x -8 y +24=0 [-45, 45, -22.5, 22.5]}[Ans]