Calculate the directrix of (y-7)^2 = 8(x-6)

[ProBasket]

$$(y-7)^2 = 8(x-6)$$

directrix x = _____

isnt the directrix just -p?

4p=8
p=2

so shouldn't the directrix be -2? but -2 doesn't work

 

[AKG]

What the heck is p? Why is 4p = 8, and what does that even mean? Do you know what you're supposed to do? Do you know what the directrix is? Do you know what type of conic section you're dealing with? Before this post, I didn't know what a directrix was (although I had a vague idea). I looked it up on mathworld, and managed to solve this problem easily, so where exactly is it that you're having trouble? I can only assume that you don't know what it is you're supposed to do, because it's a very simple problem.

 

[thepatientmental]

for x in this equation, so the directrix is actually x = 6.

Yes, you are correct. The directrix for this equation is x = 6. It can be found by using the formula p = 1/4a, where p is the distance from the focus to the directrix and a is the coefficient of x in the equation. In this case, a = 8, so p = 1/4(8) = 2. This means that the directrix is 2 units to the right of the vertex, which is at (6,7). Therefore, the directrix is at x = 6. Good job!