The centre of an ellipse is at (0,0) , major axis is on the y -axis. If the ellipse passes through (3,2) and (1,6) , then what is its eccentricity?

Step-by-step solution

Let equation of ellipse is x^2 b^2 + y^2 a^2 =1 It passes through (3,2) and (1,6) 9 b^2 + 4 a^2 =1 ...(i) 1 b^2 + 36 a^2 =1 ...(ii) Solving equations (i) and (ii), we get a^2=40 and b^2=10 Eccentricity of ellipse = 1- b^2 a^2 = 1- 10 40 = 3 2