The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².
How to determine the standard form of the equation of the parabola
In accordance with the information presented in the statement, we find a parabola whose axis of symmetry is parallel to the y-axis. The location of the vertex is the midpoint of the segment between the focus and a point of the directrix.
V(x, y) = 0.5 · (- 3, 4) + 0.5 · (- 3, 2)
V(x, y) = (- 3, 3)
The distance between the focus with respect to the vertex (p) is:
D(x, y) = F(x, y) - V(x, y)
D(x, y) = (- 3, 2) - (- 3, 3)
D(x, y) = (0, - 1)
Which a distance equal to - 1.
The standard form of the equation of the parabola is based on this model:
4 · p · (y - k) = (x - h)² (1)
Where (h, k) are the coordinates of the vertex.
If we know that (h, k) = (- 3, 3) and p = - 1, then the standard form of the equation of the parabola is:
- 4 · (y - 3) = (x + 3)²
The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².
Remark
The statement has typing and orthographical mistakes. Correct form is presented below:
What is the standard form of the equation of the parabola with a focus at (x, y) = (- 3, 2) and directrix at y = 4.
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