Question

Which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)?

Answer 1

The answer will be x squared over 4 plus y squared over 8 equals 1.

What is an ellipse?

An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.

The general equation of the ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

Hence the answer will be x squared over 4 plus y squared over 8 equals 1.

To know more about an ellipse follow

brainly.com/question/16904744

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