*CORRECTION*
I am supposed to find the 4 vertices of the ellipse
1=(((x+1)^2)/4)+(((y-4)^2)/9)
How would I go about doing that?
To find the vertices of an ellipse, you need to determine the major and minor axes of the ellipse. The equation you provided, 1 = (((x+1)^2)/4) + (((y-4)^2)/9), is in the standard form for an ellipse centered at (-1, 4).
The standard form equation for an ellipse centered at (h, k) is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h, k) represents the center of the ellipse, and a and b represent the semi-major and semi-minor axes of the ellipse, respectively.
Comparing your equation to the standard form equation, we can see that:
- The center of the ellipse is (-1, 4).
- The semi-major axis, a, is equal to 2 (since a^2 = 4, and a = 2).
- The semi-minor axis, b, is equal to 3 (since b^2 = 9, and b = 3).
The vertices of an ellipse are located at the endpoints of the major axis. In this case, the major axis is the x-axis (since the semi-major axis, a, is the larger value). Therefore, to find the vertices, you need to add and subtract the semi-major axis, a, to the x-coordinate of the center (-1).
The coordinates of the vertices of this ellipse are:
- Vertex 1: (-1 + 2, 4) = (1, 4)
- Vertex 2: (-1 - 2, 4) = (-3, 4)
So, the four vertices of the ellipse are:
(1, 4), (-3, 4)
To summarize, to find the vertices of the ellipse with the equation 1 = (((x+1)^2)/4) + (((y-4)^2)/9), you can follow these steps:
1. Identify the center of the ellipse from the equation.
2. Determine the values of the semi-major and semi-minor axes, a and b.
3. The vertices are located at a distance of a units to the left and right of the center on the x-axis.