SOLUTION: What are the vertex, focus, and dirtectrix of the parabola with the given equation? 24y = x^2

SOLUTION: What are the vertex, focus, and dirtectrix of the parabola with the given equation? 24y = x^2 - 10x + 145

Question 617173: What are the vertex, focus, and dirtectrix of the parabola with the given equation?
24y = x^2 - 10x + 145
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
What are the vertex, focus, and dirtectrix of the parabola with the given equation?
24y = x^2 - 10x + 145
complete the square
24y=(x^2-10x+25)+145-25
24y=(x-5)^2+120
(x-5)^2=24y-120
(x-5)^2=24(y-5)
This is an equation for a parabola that opens upwards.
Its standard form: (x-h)^2=4p(y-k)< (h,k)=(x,y) coordinates of the vertex.
For given equation:(x-5)^2=24(y-5)
vertex:(5,5)
4p=24
p=6
focus: (5,5+p)
=(5,5+6)
=(5,11)
directrix: y=5-p=5-6=-1

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