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

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In summary, the given equation is (y-7)^2 = 8(x-6) and the question is asking for the directrix, which can be found by solving for p in the equation 4p = 8. The directrix is then -2, but this value does not work in the equation. The person asking the question seems confused and unsure of what the directrix is and what they are supposed to do with it.
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[tex] (y-7)^2 = 8(x-6)[/tex]

directrix x = _____

isnt the directrix just -p?

4p=8
p=2

so shouldn't the directrix be -2? but -2 doesn't work
 
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  • #2
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.
 
  • #3
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!
 

1. What is the equation for finding the directrix of a parabola?

The equation for finding the directrix of a parabola is (y-k)^2 = 4p(x-h), where (h,k) is the vertex of the parabola and p is the distance between the vertex and the directrix.

2. How do you determine the directrix in a quadratic equation?

To determine the directrix in a quadratic equation, you need to find the value of p in the equation (y-k)^2 = 4p(x-h). This can be done by using the formula p = 1/4a, where a is the coefficient of the x^2 term in the quadratic equation.

3. What is the directrix in the equation (y-7)^2 = 8(x-6)?

The directrix in this equation is a horizontal line passing through the point (6,7) and is located at a distance of 1/4p units below the vertex (6,7).

4. How do you graph the directrix in a parabola?

To graph the directrix in a parabola, you need to plot the point (h,k+p) on the same side of the vertex (h,k) as the focus. Then, draw a horizontal line passing through this point to represent the directrix.

5. Can the directrix be a vertical line in a parabola?

No, the directrix in a parabola is always a horizontal line. The vertical line in a parabola is the axis of symmetry, which passes through the vertex and the focus.

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