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
The equation for an ellipse with a vertical major axis can be written as follows:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where:
- (h,k) is the center of the ellipse
- a is the distance from the center to each vertex along the x-axis
- b is the distance from the center to each co-vertex along the y-axis
In this case, the center of the ellipse is at point (0,0) since the focus is at (0,2) and the ellipse is going through 2 on the x-axis. The distance from the center to the vertex on the x-axis is 2 and the distance from the center to the co-vertex on the y-axis is 2.
Therefore, the equation for the ellipse is:
x^2/2^2 + (y-0)^2/2^2 = 1
x^2/4 + y^2/4 = 1
So, the equation of the ellipse is x^2/4 + y^2/4 = 1.