Sami Bekele
Apr 24
If y^2+2y+24x-47=0is the equation of a parabola.then what are possible?
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ChatGPT
Apr 24
If the equation y^2 + 2y + 24x - 47 = 0 represents a parabola, then the possible values for the coefficients of the equation are as follows:
1. The coefficient of y^2 must be 1, as it is the standard form of a parabolic equation.
2. The coefficient of x must be non-zero, as it determines the direction of the parabola.
3. The coefficient of y must be even, as odd coefficients would result in a non-symmetric parabola.
4. The constant term must be negative, as it determines the y-intercept of the parabola.
Therefore, possible values for the coefficients are:
y^2 + 2y + 24x - 47 = 0
1. The coefficient of y^2 must be 1, as it is the standard form of a parabolic equation.
2. The coefficient of x must be non-zero, as it determines the direction of the parabola.
3. The coefficient of y must be even, as odd coefficients would result in a non-symmetric parabola.
4. The constant term must be negative, as it determines the y-intercept of the parabola.
Therefore, possible values for the coefficients are:
y^2 + 2y + 24x - 47 = 0
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Google Gemini AI
Apr 24
The given equation is:
y^2 - 2y - 24x + 47 = 0
This can be written in vertex form as:
(y - h)^2 = 4p(x - k)
where (h, k) is the vertex and p is the distance from the vertex to the focus or directrix.
By comparing the given equation to the vertex form, we can see that:
h = 1
k = 12
p = -6
Therefore, the possible values of the vertex are (1, 12).
Since the parabola opens to the left (because p is negative), the focus and directrix are to the left of the vertex.
The focus is at a distance of p = 6 units to the left of the vertex, so the focus is at (-5, 12).
The directrix is at a distance of p = 6 units to the right of the vertex, so the directrix is at (19, 12).
y^2 - 2y - 24x + 47 = 0
This can be written in vertex form as:
(y - h)^2 = 4p(x - k)
where (h, k) is the vertex and p is the distance from the vertex to the focus or directrix.
By comparing the given equation to the vertex form, we can see that:
h = 1
k = 12
p = -6
Therefore, the possible values of the vertex are (1, 12).
Since the parabola opens to the left (because p is negative), the focus and directrix are to the left of the vertex.
The focus is at a distance of p = 6 units to the left of the vertex, so the focus is at (-5, 12).
The directrix is at a distance of p = 6 units to the right of the vertex, so the directrix is at (19, 12).
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