SOLUTION: Find the vertex, focus, equation of directrix of x^2-12x+16y=60.

Algebra ->  Bodies-in-space -> SOLUTION: Find the vertex, focus, equation of directrix of x^2-12x+16y=60.      Log On


   

Question 1111664: Find the vertex, focus, equation of directrix of x^2-12x+16y=60.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
16y-60=-x%5E2%2B12x
16y-60=-%28x%5E2-12x%29
16y-60+=-%28x%5E2-12x%2B36-36%29
16y-60=-%28%28x-6%29%5E2-36%29
16y-60=-%28x-6%29%5E2%2B36
16y-60-36=-%28x-6%29%5E2
16y-96=-%28x-6%29%5E2
highlight%2816%28y-6%29=-%28x-6%29%5E2%29

Parabola has vertex as the maximum point of the graph.
Vertical symmetry axis.

Vertex: (6,6)

Finding focus and directrix:
p, distance of vertex from focus and directrix,
4p=16
p=4
-
Focus: (2, 6)

Directrix: y=10