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Question

If r > 0, -πθπ and (r, θ) satisfy r sinθ = 3 and r = 4(1 + sinθ) then the number of possible solutions of the pair ( r, θ) is


A

2

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B

4

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C

0

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D

Infinite

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Solution

The correct option is A

2


r = 4(1 + 3r) ⇒ (r - 6)(r + 2) = 0 ⇒ r = 6, r ≠ -2 as r > 0

sin θ = 12θ = π6, 5π6

So (r, θ) = (6, π6), (6, 5π6)


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