- #1
Jarfi
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How do I find the equation of this parabola??
I am given a parabola with a "way line" l: x+y+2 = 0 and focus point F = (1;1).
How do I find it's equation?
I know I am suppost to shift it in some way and maybe mirror it, not sure how though. Need some help.
The equation of a parabole is y^2 = px, whereas x=-P/4 is the way line and F = (p/4;0) is the focus point.
I assume I am suppost to start with a parabole with focus point
F = (1;0), p = 4 and way line l: x=-1. Now I tried shifting it around (0;1) to get
F = (1;1), p = 4 and way line l: x=-2. I am almost there, but now I lack the Y, where on Earth does that Y come from? where do I go from there?
EDIT: I think going the opposite way is better but I still stop at the same spot:
I get l: x = -y -2 & F = (1;1).
1: shift around (0;-1) get:
x= -(y-1) - 2 = -y -1 & F = (1;0)
I am now closing in but all I need to do is get rid of the "-y". No idea how to do that.
EDIT:
Nevermind. I have found the solution, using the definition of a parabole lPFl = dist(p,l).
Case dismissed.
I am given a parabola with a "way line" l: x+y+2 = 0 and focus point F = (1;1).
How do I find it's equation?
I know I am suppost to shift it in some way and maybe mirror it, not sure how though. Need some help.
The equation of a parabole is y^2 = px, whereas x=-P/4 is the way line and F = (p/4;0) is the focus point.
I assume I am suppost to start with a parabole with focus point
F = (1;0), p = 4 and way line l: x=-1. Now I tried shifting it around (0;1) to get
F = (1;1), p = 4 and way line l: x=-2. I am almost there, but now I lack the Y, where on Earth does that Y come from? where do I go from there?
EDIT: I think going the opposite way is better but I still stop at the same spot:
I get l: x = -y -2 & F = (1;1).
1: shift around (0;-1) get:
x= -(y-1) - 2 = -y -1 & F = (1;0)
I am now closing in but all I need to do is get rid of the "-y". No idea how to do that.
EDIT:
Nevermind. I have found the solution, using the definition of a parabole lPFl = dist(p,l).
Case dismissed.
Last edited: