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= a ^2
but hurry up with the example :)
Question: Find an equation of the parabola with vertex at (-2, 3) and focus at (0, 3). Solution Given: The vertex (-2, 3) and focus (0, 3) both lie on the horizontal like y = 3 (the axis of symmetry). The distance \(\it a\) from the vertex to the focus is a = 2. Also, because the focus lies to the right of the vertex, the parabola opens to the right. Consequently, the form of the equation is \((y-k)^2 = 4a(x-h)\)
Sorry, was having some internet issues :)
How did they get that a = 2?
do you know how to move a point?
I don't think so
add something to it ...
Do I just need to make the -2 in the vertex 0 to find \(\it a\)?
we are given 2 points vertex at (-2, 3) and focus at (0, 3) spose we move them so the focus is at the origin (0,0) ... we would translate all points as (x+0,y-3) vertex at (-2+0, 3-3) and focus at (0+0, 3-3) vertex at (-2,0) and focus at (0,0) how far is the vertex -2 from the focus 0?
or zeroing out the vertex is fine too ... the distance would remain the same
2, so however far away the x-coordinate of the vertex is from the x-coordinate of the focus would be a?
depends on direction, but yes
Okay, I think I can do this now :)
if we zero out one point, the other will tell us how far they are from one another
v=(2,5) f=(2,-2) whats the distance and direction between them?
zero one of them out (move it to the origin) v=(2, 5) f=(2,-2) -2-5 -2 -5 ----------------- v=(0,0) f=(0,-7) -7 tells us the focus is under the vertex, and is 7 units away
ooohhh, that seems really simple, I was looking at the formulas for the equations and going "what am I supposed to use???"
Random problem from the book: v (4, -2) f (6, -2) v = (4, -2) f = (6, -2) -4, +2 -4, +2 --------------------------- v = (0, 0) f = (2, 0) So the focus is 2 units from the vertex? And 2 would be a?
very good, and the parabola opens up ... the focus is 2 above the vertex
err, 2 to the right ... opens to the right
haha that's what I was about to say :P
Thank you :3
:) the voices in my head like to tell me when im wrong
Well they must not speak very often since you're so smart :)