Question 530608: find the vertex,focus,axis and directrix of the equation
y^2-4y-4x-8=0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the vertex,focus,axis and directrix of the equation
y^2-4y-4x-8=0
complete the square
(y^2-4y+4)=4x+8+4
(y-2)^2=4x+12
(y-2)^2=4(x+3)
This is an equation of a parabola of the standard form: (y-k)^2=4p(x-h), (h,k) being the (x,y) coordinates of the vertex. Parabola opens rightwards.
For given equation:
vertex: (-3,2)
4p=4
p=1
Focus=(-3+p,2)=(-3+1,2)=(-2,2) (p units from vertex on axis of symmetry)
Axis of symmetry: y=2 (a horizontal line thru the vertex)
Directrix: x=-4 (a vertical line p units from vertex on axis of symmetry)
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