Find an equation for the ellipse whose graph has the focus at point (0,2) and the graph is going through 2 on the x axis and the center is (0,0)
The general equation of an ellipse centered at the origin with a focus at (0,c) is:
x^2/a^2 + y^2/b^2 = 1
where c is the distance from the center to the focus, and a is the semi-major axis.
In this case, since the center is at (0,0) and the focus is at (0,2), the distance from the center to the focus is c = 2.
Since the ellipse goes through (2,0) on the x-axis, we know that a = 2.
Therefore, the equation of the ellipse is:
x^2/2^2 + y^2/b^2 = 1
x^2/4 + y^2/b^2 = 1
This is the equation of the ellipse with focus at (0,2), center at (0,0), and passing through (2,0) on the x-axis.