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

Ellipse is basically the locus of a plane point in such a way that its distance from a fixed point has a constant ratio of e to its distance from a fixed line.

## Answer: the equation for the ellipse with foci (1, 1) and (−1, −1) and the major axis of length 4 is x^{2} / 4 + y^{2} /4 = 1.

Let us proceed step by step.

**Explanation:**

Here its given,

Foci = (1,1) and (-1,-1)

Major axis = 4

Now, as we know the standard equation of ellipse is

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

Since foci is (1,1) and (-1,-1) centre will be 0 that is c = 0

And vertex will be (0,0).

Also, major axis that is, 2a = 4

Therefore, a = 2

Now, we know,

a^{2} = b^{2}+ c^{2}

After putting the value, we get

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

Therefore, b^{2} = 4.

Using the standard equation, we get

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

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