Find the equation to the ellipse (referred to its axes as the axes of x and y respectively) which passes through the point (-3, 1) and has eccentricity √(2/5).

Given:

The point

   

Eccentricity

   

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

…….(i)

 

Now let us substitute equation (2) in equation (1), we get

It is given that the curve passes through the point

   

So by substituting the point in the curve we get,

   

   

Or,

   

   

From equation (2)

   

   

Or,

   

So now, the equation of the ellipse is given as:

   

∴ The equation of the ellipse is