Question

$A$ & $B$ are two fixed points. The vertex $C$ of $△ABC$ moves such that $\cot A+\cot B=$ constant. The locus of $C$ is a straight line

• A. $\perp$er to $AB$
• B. parallel to $AB$
• C. inclined to an angle to $AB$
• D. None of these

Answer 1

The correct option is B parallel to $AB$

We have $\cot A=\frac{AD}{CD},\cot B=\frac{DB}{CD}$
Now $\cot A=+\cot B=\frac{AD+DB}{CD}$
$\Rightarrow$ Constant(given) $=\frac{AB}{CD}$
$\Rightarrow CD=$ constant
(As $A,B$ are fixed points so $AB$ is a constant)
$\Rightarrow$ locus of $C$ is a straight line parallel to $AB$
Hence choice (b) is correct answer.