Question

write an equation for an ellipse centered at the origin which has foci at (0,±√14) and co-vertices at (±√2,0)

Answer 1

Answer:

The answer to your question is   $\frac{x^{2} }{2} + \frac{y^{2} }{16} = 1$

Step-by-step explanation:

Data

F ( 0, ± √14)

C (±√2, 0)

Process

1.- Calculate c

c is the distance from the center to the foci

c = √14

2.- Calculate b

b is the distance from the center to the co-vertices

b = √2

3.- Calculate a using the Pythagorean theorem

     a² = b² + c²

     a² = (√2)² + (√14)²

     a² = 2 + 14

     a² = 16

     a = 4

4.- We can conclude that it is a vertical ellipse because the foci are in the y- axis and the co-vertices are in the x-axis.

          (x - h)²/b² + (y - k)²/a² = 1

-Substitution

          (x - 0)²/(√2)² + (y - 0)²/4² = 1

- Simplification

          x²/2 + y²/16 = 1

or    $\frac{x^{2} }{2} + \frac{y^{2} }{16} = 1$