Question 884464
What is the vertex, focus, axis of symmetry, and directrix for the parabola whose equation is y2+8y+48x-32=0
complete the square:
(y2+8y+16)+48x=32+16
(y+4)^2=-48x+48
(y+4)^2=-48(x-1)
This is an equation of a parabola that opens leftward.
Its basic form of equation: {{{(y-k)^2=-4p(x-h)}}}, (h,k)=coordinates of the vertex
For given equation:
vertex: (1,-4)
axis of symmetry: y=-4
4p=48
p=12
focus: (-11,-4) (p-distance left of vertex on the axis of symmetry)
directrix: x=13  (p-distance right of vertex on the axis of symmetry)