An ellipse with its minor and major axis parallel to the coordinate axes passes through (0,0),(1,0) and (0,2) . One of its foci lies on the y-axis. The eccentricity of the ellipse is

Step-by-step solution

Centre is (x- 2 )² a² + (y- )² b² =1 pass through (0,0)(0,2) &(1,0) Distance between aligned F₁ & F₂ &=2 ae ² &=4 a ² e ² aligned Pass through (0,0) array l ² 4 a ² + ² ~b ² =1 ² 4 a ² = e ² array Pass through (0,2) ² 4 a ² + (2- )² ~b ² =1 from these two =1 Use properties PF ₁+ PF ₂=2 a array l F ₁(0,1) F ₂( , 1) P (0,2) 1+ ²+1 =2 a F ₁(0,1) F ₂( , 1) P (1,0) 1+1 + ( -1)²+1 =2 a array From these two =-2 +2 2 a put in any of above two equations array l a= 2 +1 2 2 a= 2 +1 =1 =2 ae =1,2 a = 2 +1 find e = 2 array