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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