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Write an equation for the ellipse centered at the origin with a major axis 14 units long with co-vertices at (2, 0) and (-2, 0).

a. x^2/14 + y^2/8 = 1

b. x^4/2 + y^4/49 = 1

c. x^2/4 + y^2/49 = 1

d. x^2/7 + y^2/2 = 1

Respuesta :

The equation for the ellipse centered at the origin is C. x²/4 + y²/49 = 1.

How to illustrate the information?

Let the equation of the ellipse be:

x²/b² + y²/a² = 1

The co vertices are at (2, 0) and (-2, 0). The major axis is 14 units. Therefore, 2a = 14. This implies that a = 7 and a² = 7 × 7 = 49.

Therefore, since x²/b² + y²/a² = 1, this will be x²/4 + y²/49 = 1.

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