find the equation of an ellipse that passes through the origin and has foci at (-1,1) and (1,1)

Question

Analytic geometry

Answer 1

The ellipse foci at (-1, 1) and (1,1)

The y coordinate is same in foci,so the ellipse is horizontal.

Standard form of horizontal ellipse

Center is the mid point of focus.

The ellipse passes through (0,0) and it's center is (0,1)

Substitute x = 0 , y = 0, h = 0 and k = 1 in standardform.

c is the distance from the center to each focus.

Distance between (0,1) and (1,1)

We know that

Substitute the values a², b² and (h,k) in standard form of ellipse.

The equation is .