Find an equation for the ellipse whose graph is shown with f at the point (0,2)
To find the equation of the ellipse with f at the point (0,2), we need to first identify the center and the major and minor axes of the ellipse.
From the graph, we can see that the center of the ellipse is at the point (0, 0) and the major axis is vertical with a length of 4 units (from -2 to 2) and the minor axis is horizontal with a length of 2 units (from -1 to 1).
The equation of an ellipse with center at (h, k), major axis of length 2a, and minor axis of length 2b is given by:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Plugging in the values for this ellipse, we get:
(x-0)^2/1^2 + (y-0)^2/2^2 = 1
Simplifying this, we get:
x^2 + y^2/4 = 1
Therefore, the equation of the ellipse with f at the point (0, 2) is x^2 + y^2/4 = 1.