A directrix can be viewed as a "vector" for the points of the focus of a quadratic function. In other words, like a hypotenuse, it can be calculated using Pythagorean Theorem.
Since d: x = 8, set that equal to 0
d: x-8 = 0
Same thing for the focal points:
x: x = -8 --> x+8 = 0
y: y = 0 --> y -0 = 0 --> y = 0
Now use the value of d equal to zero as the "vector" of the x and y values of the focus. In mathematical terms:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
where c = (x-8), a = (x+8), and b = (y)
[tex] {(x - 8)}^{2} = {(x + 8)}^{2} + {y}^{2} \\ {(x - 8)}^{2} = {(x + 8)}^{2} + {y}^{2} \\ {x}^{2} - 16x + 64 = \\ {x}^{2} + 16x + 64 + {y}^{2} [/tex]
Now get the x's and y on opposite sides:
[tex]{x}^{2} - 16x + 64 = \\ {x}^{2} + 16x + 64 + {y}^{2} \\ - 32x = {y}^{2} \\ x = {y}^{2} \div - 32[/tex]
therefore, D) is the correct one
[tex]x = \frac{ - 1}{32} {y}^{2} [/tex]
