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Question

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=tan1xa...(1)
y=btan(θ+β)
θ+β=tan1yb...(2)
Substract equation (2) from (1)
αβ=tan1xatan1yb
tan1xayb1+xayb=αβ

xy+ab=(bxay)cot(αβ)

Hence, it is the equation of rectangular hyperbola

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