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Prove that the common tangent of the ell...

Prove that the common tangent of the ellipses `(x^2)/(a^2)+(y^2)/(b^2)-(2x)/c=0 and (x^2)/(b^2)+(y^2)/(a^2)-(2x)/c=0` subtends a right angle at the origin.

A

`alpha = (pi)/(4)`

B

`alpha = (pi)/(2)`

C

`alpha = (3pi)/(2)`

D

none of these

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The correct Answer is:
B
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