Find the equation of the ellipse with center at the origin, the major axis on the x-axis and passing through the points

Given:

Center is at the origin

and Major axis is along x – axis

So, Equation of ellipse is of the form

   

…(i)

Given that ellipse passing through the points

   

and

   

So, point

   

and

   

will satisfy the eq. (i)

Taking point

   

where x =

   

and y =

   

Putting the values in eq. (i), we get

   

   

…(ii)

Taking point

   

where x =

   

and y =

   

Putting the values in eq. (i), we get

   

   

…(iii)

Now, we have to solve the above two equations to find the value of a and b Multiply the eq. (iii) by 16, we get

   

 

   

…(iv)

Subtracting eq. (iv) from (ii), we get

   

Substituting the value of

   

in eq. (iii), we get

_TThus,

   

Substituting the value of

   

in eq. (i), we get