SOLUTION: hello, my question is concerning parabolas. I have to find the equation of the parabola whose vertex is (4, -2) and focus at (6,-2). my teacher rushed through this section and fail

Question 170420: hello, my question is concerning parabolas. I have to find the equation of the parabola whose vertex is (4, -2) and focus at (6,-2). my teacher rushed through this section and failed to explain what exactly the focus, vertex, and directrix is. If you could please explain to me them and the equations you use for them i would really appreciate it.
Thanks!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I have to find the equation of the parabola whose vertex is (4, -2) and focus at (6,-2). my teacher rushed through this section and failed to explain what exactly the focus, vertex, and directrix is.
-----------------
Plot those two points and sketch the parabola opening to the right
starting at the vertex.
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The distance from the vertex to the focus is 6-4=2
That means p = 2,
And you already have the vertex, so h=6 and k=-2
-----------------------------------------------------
EQUATION Form:
(y-k)^2 = 4p(x-h)
Your Equation:
(y+2)^2 = 8(x-6)
----------------------
Comment: Using google on the internet will get you all the information
you need and illustrations so you can see what the vertex, directrix,
and focus are.
===================
Cheers,
Stan H.
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