Let A 2,0 and B - 2,0 are two fixed vertices of ∆ A B C . If the vertex C moves in the first quadrant in such a way that cot ⁡ A + cot ⁡ B = 2, then the locus of the point C is

Question

Let A 2,0 and B - 2,0 are two fixed vertices of ∆ A B C . If the vertex C moves in the first quadrant in such a way that cot ⁡ A + cot ⁡ B = 2, then the locus of the point C is, y = 2, x = 4, x = 2, y = 1

MARKS App · Accepted Answer

Given that, coordinates of two fixed points A and B are 2 , 0 and - 2 , 0 respectively Let variable point C is h , k . From the adjoining figure, cot ⁡ A = D A C D = 2 - h k cot ⁡ B = B D C D = 2 + h k But cot ⁡ A + cot ⁡ B = 2 , so we have 2 - h k + 2 + h k = 2 ⇒ 2 k = 1 Hence, locus of C is y = 2

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