Question 710137
what are the vertex, focus and directrix of the parabola:
12y=x^2-6x+45
x^2-6x=12y-45
complete the square:
(x^2-6x+9)=12y-45+9
(x-3)^2=12y-36
{{{(x-3)^2=12(y-3)}}}
This is an equation of a parabola that opens upwards.
Its standard form: {{{(x-h)^2=4p(y-k)}}}, (h,k)=(x,y) coordinates of the vertex.
For given parabola:
vertex: (3,3)
axis of symmetry: x=3
4p=12
p=4
focus: (3,7) (p-distance above vertex on the axis of symmetry)
directrix: y=-1 (p-distance below vertex on the axis of symmetry)