How to write the equation of a parabola given 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

[ejayvillaver]

The vertix is actually (2, -4) so the standard equation would be (x+4)^2=4(x-2)

[StealShotRemy]

He did a great job explaining. Thanks for helping!!

[DondeEstaMiManzana]

Thank you so much!! I needed this!! I feel like I understand it now 😭😭!!!

[dareal]

Im not sick of thanking you in each video really understood the conic section part i have the logic thing if you cover it I'll be happy cause I've been absent for school around 1month cause i was sick anyhow Mr you rock

[kaskadelynn]

Very concise and helpful. Thank you so much for this video!

[charleedolor]

Hi sir! What if my focus is (-6, 3) and my directrix is y=4? Pls help thanks...

[jeprefereetreaparis]

I thought FOCUS is (h, k+p) so If it's k+p then how the y-intercept is -4

[joshuagaborne]

focus(-10, 23/2), directrix y=-(11/2) need help solving standard equation if there's a fraction