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Question

The centre of the circle x = 2 + 3 cos θ, y = 3 sin θ - 1 is

A
(3, 3)
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B
(2, -1)
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C
(-2, 1)
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D
(-1, 2)
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Solution

The correct option is B (2, -1)
x = 2 + 3 cos θ, y = 3 sin θ - 1
x2+y2=4+9 cos2 θ +12 cos θ +9 sin2 θ +16 sin θ
=14+12 cos θ6 sin θ
= 4 (2 + 3 cos θ ) - 2(3 sin θ - 1) + 4
x2+y2=4x2y+4
(x24x+4)+(y2+2y+1)=9
(x2)2+(y+1)2=9, centre is (2, -1).

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