Find an equation for the ellipse whose graph is shown with foci at the point (0,2)
and (-4,2), and major axis length of 10.
The general equation for an ellipse with foci on the y-axis is:
y^2 = a^2 - x^2
In this case, the major axis length is 10, so a = 5. Since the foci are at (0,2) and (-4,2), the distance between the foci is 4. This distance is also equal to 2ae, where a = 5, so 2(5)e = 4, and e = 4/10 = 0.4.
Substitute a = 5 and e = 0.4 into the general equation:
y^2 = 25 - x^2
Therefore, the equation for the ellipse with foci at (0,2) and (-4,2), and major axis length of 10 is y^2 = 25 - x^2.