Final answer:
To find an equation for the given ellipse, we use the formula for eccentricity and the information about the foci.
Step-by-step explanation:
An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is a constant.
The eccentricity of an ellipse is calculated by dividing the distance from the center of the ellipse to one of the foci by half the length of the major axis. We can use this information to find an equation for the ellipse that satisfies the given conditions.
- First, we determine the length of the major axis of the ellipse. The distance between the foci is given as 2.5 units. Since the length of the major axis is twice the distance between the foci, the length of the major axis is 5 units.
- Next, we find the distance from the center of the ellipse to one of the foci. Since the eccentricity is 0.5 and the distance between the foci is 2.5 units, the distance from the center to one of the foci is (0.5)(2.5) = 1.25 units.
- Now, we can write the equation of the ellipse based on its standard form: x2/a2 + y2/b2 = 1. Since the eccentricity is less than 1, we know that the ellipse is elongated horizontally.
- By substituting the values we found, we get the equation of the ellipse as x2/25 + y2/8.75 = 1.