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Question

For hyperbola x225y216=1, and circle x2+y2=100, con-cyclic points are


A
±102940,±20340
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B
±102941,±20341
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C
±1041,±20341
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D
±2941,±10341
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Solution

The correct option is B ±102941,±20341
The given hyperbola x225y216=1 and given circle x2+y2=100, cut each-other at four common points, which are con-cyclic points.

From equation of circle getting y2=100x2 ....(1)

and putting value of y2 from equation (1) into equation of given hyperbola we get,

x225(100x2)16=1

x225+x216(100)16=1

41x225×16=(29)4

x=±102941

Hence,

x1=+102941

x2=102941

Now y2=100x2=100 (±102941)2

y2=100(412941)

y=±20341

So y1=+20341

y2=20341

Hence con-cyclic point of given hyperbola and circle are:

±102941, ±20341

Correct option is B.

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