Find the equation of the ellipse, with major axis along the x-axis and passing through the points (4, 3) and (– 1, 4).

The standard form of the ellipse is x²/a² + y²/b² = 1. Since the points (4,3) and (-1,4) lie on the ellipse, we have

16/a² + 9/b² = 1   … (1)

and

1/a² + 16/b² = 1   ….(2)

/Solving equations (1) and (2), we find that a² =247/7 and b² = 247/15.

∴ The required equation is x²/(247/7) + y²/247/15 = 1

i.e., 7x² + 15y² = 247.