Give the coordinates of the center, foci, vertices, and covertices of the ellipse
with the given equation. Sketch the graph, and include these points.
4(x
+ 2) 2 +
(y+4)
2
4
= 1
Cannot graph on these posts.
Also, it is very difficult to make sense about data in a vertical orientation.
geez, just type your stuff, ok? This copy/paste is useless, wheever you're doing it from.
Recall that if a>b
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
has
center at (h,k)
vertices at (h±a,k)
covertices at (h,k±b)
foci at (h±c,k) where c^2 = a^2 - b^2
type in your equation at wolframalpha.com
it will show the graph.
Click on the "properties" button to see data about the items of interest
To find the coordinates of the center, foci, vertices, and covertices of the given ellipse, we can start by examining its equation.
The standard equation of an ellipse is given by:
((x - h)² / a²) + ((y - k)² / b²) = 1,
where (h, k) represents the coordinates of the center, 'a' represents the distance from the center to the vertices, and 'b' represents the distance from the center to the covertices.
Comparing the given equation, 4(x+2)² + (y+4)²/4 = 1, with the standard equation, we can identify the values as follows:
Center: The center of the ellipse is (-2, -4). This is evident from the values of (h, k) in the equation.
Vertices: The distance from the center to the vertices is represented by 'a', which can be found as the square root of the denominator of the x-term. In this case, a = √4 = 2.
Therefore, the vertices are located at (-2 + 2, -4) and (-2 - 2, -4), giving us the coordinates (-0, -4) and (-4, -4) respectively.
Covertices: The distance from the center to the covertices is represented by 'b', which can be found as the square root of the denominator of the y-term. In this case, b = √4 = 2.
Therefore, the covertices are located at (-2, -4 + 2) and (-2, -4 - 2), giving us the coordinates (-2, -2) and (-2, -6) respectively.
Foci: To find the foci, we can calculate 'c', which is the distance from the center to the foci. It can be found using the equation c = √(a² - b²). In this case, c = √(4 - 4) = √0 = 0. Since 'c' is zero, the foci coincide with the center of the ellipse. Therefore, the foci have the same coordinates as the center, which are (-2, -4).
Now that we have the coordinates of the center (-2, -4), foci (-2, -4), vertices (-0, -4) and (-4, -4), and covertices (-2, -2) and (-2, -6), we can sketch the graph of the ellipse using these points.