How to write the equation of a parabola given the focus and directrix

Learn how to write the equation of a parabola given the focus and the directrix. A parabola is the shape of the graph of a quadratic equation. A parabola can open up or down (if x is squared) or open left or right (if y is squared). Recall that the focus and the vertex of a parabola are on the same line of symmetry.

When given the focus and the directrix of a parabola, recall that the vertex of a parabola is halfway between the focus and the directrix and the focus is inside the parabola. This enables us to identify the direction which the required parabola opens. We also need to identify the value of p, which is the distance between the vertex and the focus. p is negative when the parabola opens down or left and is positive when the parabola opens right or up.

Once we identify the direction and the value of p, we can use the equation of parabola given by (y - k)^2 = 4p(x - h) for parabolas that opens up or down and (x - h)^2 = 4p(y - k) for parabolas that opens left or right.
#conicsections #parabolaconicsections

[amarahmed]

better than my algebra teacher... Thanks man... U make math fun, unlike my algebra teacher😒

[danieldanmola]

Sir, you made a mistske,
Vertex should be ( 4, 2)
Moreover, the y coordinate of a vertex should have the same y coordinate as the focus

[Yoo-ov]

The graph represent the equation: (x-h)^2=-4p(y-k) but I want to ask why did you use (x-h)^2=4p(y-k) (without the negative sign)?

[Top-rvn]

Why is the (x- -2)^2 is equal to (x+2)^2? please answer. I am really confused