x^2/16 - (y^2+4) = 1
Vertices: (4,-4)(-4,-4)
Foci: (4.1,1)(-4.1,1)
am i right?
To check if your answer is correct, let's first understand the equation of the ellipse.
The general equation for an ellipse centered at the origin (0,0) can be written as:
(x^2/a^2) + (y^2/b^2) = 1
In this equation, 'a' represents the distance from the center to the horizontal vertices of the ellipse, and 'b' represents the distance from the center to the vertical vertices of the ellipse.
To compare this with the given equation:
x^2/16 - (y^2+4) = 1
We can see that the coefficient of x^2 is 1/16, so a^2 = 16, which means a = 4.
The coefficient of y^2 is -1, so b^2 = -1. However, the square of any real number cannot be negative, so there is an error in the equation.
Since the equation is not in the standard form of an ellipse, we need to rearrange it. Let's bring all the terms to one side of the equation:
x^2/16 - (y^2+4) - 1 = 0
Now, let's simplify the equation:
x^2/16 - y^2 - 5 = 0
To find the vertices, we need to add/subtract 'a' from the x-coordinate of the center and keep the y-coordinate the same. So, we have:
Vertex 1: (4, -4)
Vertex 2: (-4, -4)
Now, to find the foci, we need to calculate the value of 'c', which is the distance between the center and the foci. The formula is:
c^2 = a^2 - b^2
Here, we know a = 4, but since b^2 = -1 (which is incorrect), we cannot determine the value of 'c'.
As a result, it seems that there might be an error in the given equation or in the values provided for the foci. Without the correct equation or additional information, we cannot determine the accuracy of your answer regarding the foci.