SOLUTION: parabola- sketch the parabola (y-1)^2 = 8(x-2) showing clearly all points and labeling, marking clearly the directrix, focus and vertex.

Algebra ->  Coordinate-system -> SOLUTION: parabola- sketch the parabola (y-1)^2 = 8(x-2) showing clearly all points and labeling, marking clearly the directrix, focus and vertex.      Log On


   

Question 1101490: parabola- sketch the parabola (y-1)^2 = 8(x-2) showing clearly all points and labeling, marking clearly the directrix, focus and vertex.
Found 3 solutions by josgarithmetic, greenestamps, richwmiller:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
4%2A2=8
vertex, (2,1)
and form of equation means that symmetry axis horizontal; parabola opens toward the right.
focus, (4,1)
directrix, x=0 or (0,y).

y=1%2B-+sqrt%288%28x-2%29%29

graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C1-sqrt%288x-16%29%2Csqrt%288x-16%29%29

Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


With the y variable squared, this parabola opens horizontally; with the coefficient on the x term positive, it opens to the right.

The standard vertex form (that I use!) for a parabola that opens horizontally is

%28x-h%29+=+%281%2F%284p%29%29%28y-k%29%5E2%29

or

%28y-k%29%5E2+=+4p%28x-h%29

In this form, p is the distance from the vertex to the focus, and from the vertex to the directrix.

The equation for your parabola is
%28y-1%29%5E2+=+8%28x-2%29

That means p is 2; so the vertex of the parabola is at (2,1); the focus is 2 units to the right of the vertex, at (4,1); and the directrix is the vertical line 2 units to the left of the vertex, x=0.





(Sorry.... I haven't yet figured out how to do labeling on a graph....)

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
To label use locate as Edwin did in the next problem.
(Trigonometry-basics/1101510:)
locate(0,0,B),locate(5,0,C), locate(.6,2.8,A)
locate(.1,1.2,c),locate(2.5,1.7,b=5m), locate(2,0,a=5m)
The first two entries are the x, y and the third entry is your label