Find the equation of the ellipse with center at the origin, the major axis on the x-axis and passing through the points (4, 3) and (-1, 4).

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 (4, 3) and (-1, 4)

So, point (4, 3) and (-1, 4) will satisfy the eq. (i)

Taking point (4, 3) where x = 4 and y = 3

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

…(ii)

Taking point (-1, 4) where x = -1 and y = 4

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 b² in eq. (iii), we get

Thus,

Substituting the value of a² and b² in eq. (i), we get

⇒ 7x² + 15y² = 247