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A and B are fixed points such that AB=2a...

A and B are fixed points such that AB=2a. The vertex C of `DeltaABC` such that `cotA+cotB`=constant. Then locus of C is

A

straight line perpendicular to AB

B

straight line parallel to AB

C

circle

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`cot A +cotB=` constant
`rArr (AD)/(CD)+(BD)/(CD)=` constant, (where D is the foot of perpendicular from C to AB)
`rArr (AD+BD)/(CD) =` constant
`rArr (2a)/(CD) =` constant
`rArr CD =` constant
C is moving at a constant distance from AB
`:.` locus of C is a line parallel to AB
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