What is the correct standard form of the equation of the parabola?
Enter your answer below. Be sure to show each step of your work.
Where the parabola is (2,-4)
To determine the standard form of the equation of a parabola, we need additional information such as the vertex and the focus of the parabola.
Given that the parabola passes through the point (2, -4), we can infer that this point lies on the parabola. However, without any other information, we cannot determine the standard form of the equation of the parabola.
the diretix is (2,-5)
To find the equation of a parabola given its vertex (h, k) and directrix, we can use the formula:
(x - h)^2 = 4p(y - k)
where (h, k) is the vertex and (h, k + p) is the focus, and p is the distance between the vertex and the focus.
The given vertex is (2, -4), and the given directrix is the point (2, -5).
Since the directrix is a horizontal line, the parabola opens either upwards or downwards. Let's assume it opens upwards.
The vertex form of the equation becomes:
(x - 2)^2 = 4p(y + 4)
To find the value of p, we need to calculate the distance between the vertex and the directrix. Since the parabola opens upwards, p is positive and is equal to the distance between the vertex and the directrix.
Using the distance formula, we have:
p = |-5 - (-4)| = |-5 + 4| = |1| = 1
Substituting this value of p into the equation, we get:
(x - 2)^2 = 4(1)(y + 4)
(x - 2)^2 = 4y + 16
x^2 - 4x + 4 = 4y + 16
Expanding and rearranging the equation, we have:
x^2 - 4x - 4y - 12 = 0
Therefore, the standard form of the equation of the parabola with the vertex (2, -4) and directrix (2, -5) is:
x^2 - 4x - 4y - 12 = 0
To find the standard form of the equation of the parabola, we need to have additional information, such as the vertex or the focus. The given point (2,-4) alone is not enough to determine the equation in standard form.
The standard form of the equation of a parabola is given by:
y = a(x-h)^2 + k
Where (h,k) represents the vertex of the parabola.
If you provide additional information, such as the vertex or the focus, I can help you find the standard form of the equation.
To find the standard form of the equation of a parabola, we need additional information such as the focus or directrix. Without this additional information, it is not possible to determine the standard form equation of the parabola.
A parabola can be represented in standard form as follows:
(x - h)² = 4p(y - k)
Where (h, k) is the vertex of the parabola, and p is the distance between the vertex and the focus or vertex and the directrix.
Given that the vertex is (2, -4) alone, we cannot determine the equation in standard form without knowing the focus or directrix.