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The eccentricity of the ellipse which meets the straight line x 7 + y 2 =1 on the axis of x and the straight line x 3 - y 5 =1 on the axis of y and whose axes lie along the axes of coordinates is 2 6 . Find

Correct answer

07

Step-by-step solution

x^2 a^2 + y^2 b^2 =1 ...(1) x 7 + y 2 =1 meets x -axis at A(7,0) , line x 3 - y 5 =1 meets y -axis at B(0,-5) . (1) passes through A & B aligned & 49 a ^2 +0=1,0+ 25 ~b ^2 =1 & a ^2=49, ~b ^2=25 ; b ^2= a ^2 (1- e ^2 ) 25=49 (1- e ^2 ) & e ^2= 24 49 e = 2 6 7 aligned

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