If the foci x2a2−y2b2=1coincide with the foci of x225+y29=1 and the eccentricity of the hyperbola is 2, then

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a2+b2=16

there is no director circle to the hyperbola

the center of the director circle is (0, 0)

the length of latus rectum of the hyperbola is 12

answer is A.

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Detailed Solution

For the ellipse, a=5 and e=25−925=45∴ ae=4Hence, the foci ate (-4, 0) and (4, 0)'For the hyperbola, ae=4,e=2∴ a=2 b2=4(4−1)=12 or b=12

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