Question

Find the equation of the ellipse whose foci are (4, 0) and (- 4, 0), eccentricity = 1/3.

Answer 1

Given:

Foci are (4, 0) (- 4, 0)

Eccentricity = 1/3.

Now let us find the equation to the ellipse.

We know that the equation of the ellipse whose axes are x and y – axis is given as

By using the formula,

Eccentricity:

It is given that foci = (4, 0) (- 4, 0) => foci = (±ae,0)

Where, ae = 4

a(1/3) = 4

a = 12

a² = 144

By substituting the value of a², we get

b² = 8a²/9

b² = 8(144)/9

= 128

So the equation of the ellipse can be given as

So, the equation of the ellipse is