SOLUTION: Find the features of the parabola which is x2+8x-18-6y=0. Find the vertex the focus the directrix the axis of symmetry and graph it...

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the features of the parabola which is x2+8x-18-6y=0. Find the vertex the focus the directrix the axis of symmetry and graph it...       Log On


   

Question 1020336: Find the features of the parabola which is x2+8x-18-6y=0. Find the vertex the focus the directrix the axis of symmetry and graph it...
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square to get into vertex form,
x%5E2%2B8x-18=6y
x%5E2%2B8x%2B16-18=6y%2B16
%28x%2B4%29%5E2-34=6y
y=%28x%2B4%29%5E2%2F6-34%2F6
y=%28x%2B4%29%5E2%2F6-17%2F3
Vertex is (-4,-17%2F3)
The axis of symmetry is x=-4
Switch to focus form,
%28x%2B4%29%5E2=6y%2B34
%28x%2B4%29%5E2=6%28y%2B17%2F3%29
So then the focus is,
(h,k+p) where p=6.
(-4,-17%2F3%2B18%2F3)
(-4,1%2F3)
The directrix is then,
y=k-p
y=-17%2F3-18%2F3
y=-35%2F3
.