How do you find the equation of a parabola giving the focus and directix

Explanation:

There are a few things to remember for this:

You may see more complicated formulas that have you plug in focus and directrix values. I find it easier to remember the above, since it involves the vertex form you've already seen: y = a(x -h)^2 +k. The "trick" is that the scale factor (a) is 1/(4p).

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If you're graphing the result, as a check on your work, you can make sure that the parabola matches its geometric definition. The distance from any point on the parabola to the focus is the same as the distance from that point to the directrix. This is why the vertex is halfway between the focus and directrix: so the distances are the same.

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Example:

Focus (1, -3); directrix y=5.

Distance from focus to directrix: -3-5 = -8, so p = -4. The vertex is (1, 1), and the equation is ...

  y = -1/16(x -1)^2 +1

details

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it