The eccentricity of the ellipse, which meets the straight line x7+y7=1 on the axis of x and the straight line x3−y5=1 on the axis of y and whose axes lie along the axes of coordinates, is
A
3√27
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B
2√67
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C
√37
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D
None of these
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Solution
The correct option is A2√67 Let the equation of the ellipse be x2a2+y2b2=1
By using
It is given that it passes through the lines x+y=7 and 5x−3y=15
So, it passes through the points (7, 0) and (0, -5).
Therefore, a2=49 and b2=25
The eccentricity of the ellipse is given by e=√1−b2a2=√1−2549=√2449=2√67