Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half

Question

imstuck · Answer

Do you know much about parabolas and their standard form?  Can you tell which type it by looking at it (vertical or horizontal)?  These are nice and easy once you get the hang of them because they are all done the same way.

solomonzelman · Answer

you should be able to write out the equation of the parabola, once you are up to deriving.

imstuck · Answer

I don't think he means deriving like in Calculus, I think he means just coming up with the proper equation for the parabola with those specific characteristics.  Hmmm, right?  Let's see what he has to say about this!

anonymous · Answer

PARABOLAAAAAAAAAAAAAAAAAAAAAA (The more you know) 

|dw:1402447161421:dw|


|dw:1402447391588:dw|

A parabola is the set of all points at an equal distance from a fixed point and a fixed line.

Well there's two kinds I guess you could say, Horizontal, and vertical.

Horizontal (y term is squared)

$$(y-k)^2=4p(x-h)$$

Vertical ( x term is squared)

Vertex (h, k)

p = distance and direction from vertex to focus, distance and opposite direction from vertex to directrix.

Note: There is NO CENTRE. One vertex and it's on the parabola.

I'll show you some examples now....