What are the focus and vertex of the parabola described by #y^2+6y+8x+25 = 0#?

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Answer 1 · 2018-05-05T12:39:54

Vertex is at # (-2 ,-3)#
Focus is at # (-4 ,-3)#

#y^2+6 y+8 x+25 = 0# or

#y^2+6 y= -8 x-25 # or

#y^2+6 y +9 = -8 x-25 +9 # or

#(y+3)^2 = -8 x-16 # or

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

The equation of horizontal parabola opening left is

#(y-k)^2 = -4 a (x-h) :. h=-2 ,k= -3 , a= 2#

Vertex is at #(h,k) # i.e at # (-2 ,-3)#

Focus is at #((h-a),k) # i.e at # (-4 ,-3)#

graph{y^2+6 y +8 x +25 =0 [-40, 40, -20, 20]}