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

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

The standard equation of the ellipse is

(x - h)^{2} / a^{2} + (y - k)^{2} / b^{2} = 1

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

Substituting the values

2^{2} = b^{2}+ 0^{2}

b^{2} = 4

Now substitute the values in the standard equation

(x - 0)^{2} / 4 + (y - 0)^{2} / 4 = 1

x^{2}/4 + y^{2}/4 = 1

Therefore, the equation of the ellipse is x^{2}/4 + y^{2}/4 = 1.

## 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 x^{2}/4 + y^{2}/4 = 1.