Final answer:
To find an ellipse with the given foci and vertex, use the distance formula to determine the values of a and c. Then, plug these values into the equation for an ellipse and solve for b to get the final equation.
Step-by-step explanation:
To find an ellipse with foci (0,+-1) and vertex (0,2), we can use the distance formula. The distance from the center of the ellipse to one of its foci is called the c-value. Since the foci are at (0,+-1), the c-value is 1. The distance from the center to a vertex is called the a-value. Since the vertex is at (0,2), the a-value is 2.
Now, using the formula for an ellipse, we have the equation: x2/a2 + y2/b2 = 1. Plugging in the values a = 2 and c = 1, we can solve for b:
22/b2 + 1/b2 = 1
Simplifying this equation, we have: 4/b2 + 1/b2 = 1
Combining like terms, we get: 5/b2 = 1
So, b2 = 5. The equation of the ellipse is then: x2/4 + y2/5 = 1.