P lies inside both x 2 + y 2 − 4 = 0 and x 2 + y 2 − 8 x + 7 = 0 . It moves at a fixed distance from a fixed point in their common region, and its path encloses the greatest possible area. Find its lo

Question

P lies inside both x 2 + y 2 − 4 = 0 and x 2 + y 2 − 8 x + 7 = 0 . It moves at a fixed distance from a fixed point in their common region, and its path encloses the greatest possible area. Find its locus.

TestHub · Accepted Answer

The boundary circles have centres ( 0 , 0 ) , radius 2 and ( 4 , 0 ) , radius 3 . The largest circle inside their common lens is centred at ( 3/2 , 0 ) with radius 1/2 , touching both internally. The locus is ( x − 3/2 ) 2 + y 2 = 1/4 , i.e. x 2 + y 2 − 3 x + 2 = 0 .

Mathematics - Circle Question with Solution | TestHub

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