Hi,

 x^2-6x-8y+49=0

8y = (x-3)^2 + 40

 y = (1/8)(x-3)^2 + 5   Parabola opening right, y = 5, line of symmetry

V(3,5),  , , Focus(5,5), Directrix x = 1 

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
 Identify the vertex, focus and directrix of the parabola with the equation x^2-6x-8y+49=0

***

x^2-6x-8y+49=0

x^2-6x-8y=-49

complete the square:

(x^2-6x+9)-8y=-49+9

(x-3)^2=8y-40

(x-3)^2=8(y-5)

This is an equation of a parabola that opens up:

Its basic equation: (x-h)^2=4p(y-k), (h,k)=coordinates of vertex

For given problem:

vertex:(3,5)

axis of symmetry: x=3

4p=8

p=2

focus: (3,7)(p-distance above vertex on the axis of symmetry)

directrix: y=3(p-distance below vertex on the axis of symmetry)



see graph below as a visual check:





 

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