The coordinates of a point are atan(θ+α) and btan(θ+β), where θ is variable, then locus of the point is
A
hyperbola
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B
rectangular hyperbola
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C
ellipse
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D
None of the above
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Solution
The correct option is B rectangular hyperbola x=atan(θ+α) ⇒θ+α=tan−1xa...(1) y=btan(θ+β) ⇒θ+β=tan−1yb...(2) Substract equation (2) from (1) α−β=tan−1xa−tan−1yb ⇒tan−1xa−yb1+xa⋅yb=α−β
⇒xy+ab=(bx−ay)cot(α−β)
Hence, it is the equation of rectangular hyperbola