Question

How can the equation of a parabola be derived when given the focus and the directrix?

Answer 1

Answer:

• If the focus is to the right of the directrix, then the parabola opens to the right and p>0 . If the focus is to the left of the directrix, then the parabola opens to the left and p<0 .

HOPE ITS HELP

Answer 2

Answer:

Step-by-step explanation:

You should probably graph them both and take a look at them. The vertex will be the point exactly in the middle. Find the vertex by observation or calculate with midpoint formula. Then you will want to note in which direction the parabola is opening. Up, down, even left or right. The parabola will open away from the directrix. The focus should be nestled in the u-shaped curve of the parabola. Parabolas that open in the y direction (up or down) have formulas that begin with a y=

Parabolas that open in the x direction (left or right) have formulas that begin with a x=

Use the vertex form of the formula for a parabola.

y = a(x-h)^2 +k OR

x = a(y-k)^2 +h

Fill the coordinates of the vertex (h, k) in the formula. Lastly calculate a.

a = 1/(4p) Look back at you graph or sketch and find the distance from the vertex to the focus. That is the value of p. Use it to calculate a. Put the a you find into your vertex form equation. When you're done, you should have the a and the h and the k filled into the equation. Double check that your a value is negative if your parabola opens in a negative direction (down or left)