The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points 4 , - 1 and - 2 , 2 is

Step-by-step solution

Equation of ellipse whose centre at 0 , 0 is x 2 a 2 + y 2 b 2 = 1 It passes through ( 4 , − 1 ) ⇒ 16 a 2 + 1 b 2 = 1 ⇒ 16 b 2 + a 2 = a 2 b 2   . . . i Again it passes through ( − 2 , 2 ) ⇒ 4 a 2 + 4 b 2 = 1 ⇒ 4 b 2 + 4 a 2 = a 2 b 2   . . . i i From the equation i and i i , we get, 16 b 2 + a 2 = 4 a 2 + 4 b 2 ⇒ a 2 = 4 b 2 Now, we have, e 2 = 1 - b 2 a 2 = 1 - 1 4 = 3 4 ⇒ e = 3 2 .