Find an equation for the ellipse whose graph is shown. Foci is at point (0,2)
The equation for an ellipse with foci at (0,±c) and major radius a is:
x^2/a^2 + (y-c)^2/b^2 = 1
In this case, since the foci is at (0,2), c = 2. This implies that the major axis lies along the y-axis.
Looking at the graph, we can see that the major axis has length 4 and the minor axis has a length of 2. Therefore, a = 2 and b = 1.
Plugging these values into the equation gives us:
x^2/2^2 + (y-2)^2/1^2 = 1
Simplifying gives us:
x^2/4 + (y-2)^2 = 1
Therefore, the equation of the ellipse is:
x^2/4 + (y-2)^2 = 1