Find the equation of an ellipse whose major axis is along the y-axis and which passes through the points P (2, 2) and Q (1, 4).

The major axis is along the y-axis.
∴ The equation of ellipse in the standard form is                   ...(i)
It passes through (2, 2)                                                  ...(ii)
It passes through (1, 4)                                                   ...(iii)
Multiplying both sides of (ii) by 4, we get
                                                                                           ...(iv)
Subtracting (iv) from (iii), we get                           
∴ From (iii),   
Hence, from (i), the equation of ellipse is: