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Question

# The line y=x intersects the hyperbola x29−y225=1 at the points P and Q. The eccentricity of ellipse with PQ as major axis and minor axis of length 5√2 is

A
53
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B
53
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C
59
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D
259
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Solution

## The correct option is A √53Line y=x intersects hyperbola x29−y225=1 at P and Q putting y=x in eq. of parabola x29−y225=1 16y2=9×25 y=±3×54 x=±3×54PQ = Distance b/w points (+154,+154) and (−154,−154) =√(152)2+(152)2 =15√2Length of major axis ⇒15√2, length of minor axis =5√2 e=        ⎷1−(5√2)2(15√2)2⇒e=√200225⇒2√23

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