Find an equation for the ellipse with foci (1, 1) and (-1, -1) and the major axis of length 4?

Solution:

Foci of the ellipse = (1, 1) and (-1, -1)

Length of major axis = 4

The standard equation of the ellipse is

(x - h)² / a² + (y - k)² / b² = 1

As the foci is (1, 1) and (-1, -1) the center is 0

Vertex (h, k) = (0, 0)

We know that

Major axis = 2a = 4

a = 2

We know that

a² = b²+ c²

Substituting the values

2² = b²+ 0²

b² = 4

Now substitute the values in the standard equation

(x - 0)² / 4 + (y - 0)² / 4 = 1

x²/4 + y²/4 = 1

Therefore, the equation of the ellipse is x²/4 + y²/4 = 1.

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Find an equation for the ellipse with foci (1, 1) and (-1, -1) and the major axis of length 4?

Summary:

An equation for the ellipse with foci (1, 1) and (-1, -1) and major axis of length 4 is x²/4 + y²/4 = 1.