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

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

A

perpendicular to AB

B

parallel to AB

C

inclined at an angle A-B to AB

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`cot A= (AD)/(CD) and cot B= (DB)/(CD)`

`rArr cot A + cot B = (AD+ DB)/(CD)`
`rArr " Constant" = (AB)/(CD)`
`rArr CD = " constant"`
`rArr` Locus of C is a striaght line parallel to AB.
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