Respuesta :
Answer
1) Horizontal directrix.
2) Vertical directix.
3) Horizontal directix.
4) Vertical directrix.
Explanation
A parabola with a vertical axis will have a horizontal directrix.
A parabola with a horizontal axis will have a vertical directrix.
A parabola with a vertical axis will have a standard equation of the parabola as
(x - h)² = 4p (y - k),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h, k + p).
The directrix is the line y = k - p and it is a vertical directrix.
A parabola with a horizontal axis will have a standard equation of the parabola as
(y - k)² = 4p (x - h),
where p ≠ 0.
The vertex of this parabola is at (h, k). The focus is at (h + p, k).
The directrix is the line x = h - p and it is a horizontal directrix.
So, for this questions,
1.) (y - 3)² = 1/8 (x + 1)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
2.) (x - 2)²= 6 (y - 3)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
3.) (y + 4)² = -12 (x + 2)
This is of the form (y - k)² = 4p (x - h), so, we can easily see that this parabola has a horizontal directrix.
4.) (x+3)²= -8(y+2)
This is of the form (x - h)² = 4p (y - k), so, we can easily see that this parabola has a vertical directrix.
Hope this Helps!!!
