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Find the centre and radius of the circle x² + y² + 2x sin(theta) + 2y cos(theta) - 8 = 0.

1. Centre (-sin(theta), -cos(theta)), radius 3
2. Centre (sin(theta), cos(theta)), radius 3
3. Centre (-sin(theta), -cos(theta)), radius sqrt(8)
4. Centre (-2 sin(theta), -2 cos(theta)), radius 3

Correct answer: Centre (-sin(theta), -cos(theta)), radius 3

Solution

Here g = sin(theta), f = cos(theta), c = -8, so centre is (-sin(theta), -cos(theta)) and radius = sqrt(sin²(theta) + cos²(theta) + 8) = sqrt(9) = 3.

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