Q.
A and B are two fixed points in a ΔABC If its vertex C moves in such a way that cotA+cotB=λ where λ is constant. Then the locus of the point C is
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a
yλ=2a.
b
ya=2λ
c
y=λa
d
ya=4λ
answer is A.
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Detailed Solution
We may suppose that coordinates of two fixed points A,B are (a,0) and (−a,0) respectively and coordinates of the variable point C are (h,k)In ΔCDA cotA=DACD=a−hk andIn ΔDBC, cotB=BDCD=a+hkBut cotA+cotB=λSo we have a−hk+a+hk=λ⇒ 2ak=λ ⇒ 2a=kλ∴ Locus of C is λy=2a or y=2aλ.
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