Question

Could someone explain how to find a driectrix of a parabola? X=\frac{1}{8}Y^2

Answer 1

@Vocaloid

Answer 2

first multiply both sides by 8 to convert to standard form

8x = y^2

then compare to the standard form:

4px = y^2

so if we put

8x = y^2 and 4px = y^2 side by side we see that

8x = 4px

making p = 2

the directrix = -p = -2 = your sol'n

Answer 3

as an addendum this method only works if the vertex is right at (0,0) like it is in our problem

Answer 4

I see that when I look at it when I graph it so this method would only work if the vertex is at zero?

Answer 5

yeah

if it's not at the vertex, you will perform a similar calculation (to find p) but there are a few more steps

Answer 6

(h,k) are the coordinates of the vertices (which you will need to find from the equation), then the focus is (h + p,k) for sideways parabolas and (h, k+p) for up/down parabolas

Answer 7

So when you say compare to the standard form what are you meaning?

Answer 8

Like subtraction it from the original or dividing it?

Answer 9

like, when we put these two expressions side by side

8x = y^2

and

4px = y^2

we can see that 8x must be equal to 4px

Answer 10

"compare to standard form" just means take the equation and put it side by side with the standard form equation 4px = y^2 to see which parts correspond to each other

Answer 11

the "4px" and the "8x" parts correspond, so we can set them equal to each other which is how we solve for p

Answer 12

im just so lost to where you got 4x I cant wrap my head around it. Im sorry I have trouble understanding these things sometimes.

Answer 13

"4px = y^2" is just the standard form equation for a parabola, you just have to know/memorize this

the equation being discussed in the problem is 8x = y^2

since both equations equal y^2 we know that 8x and 4px are equal

hope that makes a little more sense

Answer 14

Oh, ok I totally understand now. I kind of figured that was the case, and thanks this has been super helpful so far, and im huessing you just get rid of the y^2 then correct?

Answer 15

yeah sort of, it's like this:

if A = B and C = B then A and C are equal since they're both equal to be

same logic with our problem, 4px and 8x are both equal to y^2 so 4px = 8x

Answer 16

*equal to B

Answer 17

Thank you so much :D this has really helped a ton!