conic

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a circle 'c' intersecting the ellipse x²/16 + y²/9=1 such that common chord is of max. length , and intersecting the circle x²+y²-6x-10y+9=0 orthogonally ,then number of common tangents of circle 'c' and circle x²+y²-10x-11=0 is-----

#Mathematics #Co-ordinate Geometry

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jeetopper jee ·2010-11-18 05:35:03

the answer is 2.
If the chord is to be of max length then it must pass thru extremities of major axis.
from this we get g=0 n c=-16 in gen equation of circle c.
also find the value of f thru orthogonality condition.
Now on comparing the equation of this circle with the circle given it is found the the circle passes thru its centre so only 2 tangents r possible.

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