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Question

# Find the parametric equation of the circle x2 + y2 âˆ’ 2x + 4y âˆ’ 11 = 0

A

x=2 + 4 cosθ and y=+4 + 4 cosθ

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B

x=2 + 4 cosθ and y=+4 + 4 cosθ

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C

x=1 + 4 cosθ and y=+2 + 4 sinθ

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D

x=1 + 4 cosθ and y=2 + 4 sinθ

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Solution

## The correct option is D x=1 + 4 cosθ and y=−2 + 4 sinθ To write the parametric equation of circle, we have to know the centre and radius of the circle. If the centre is (h, k) and radius is r, the parametric equation of the circle is given by x=h + r cosθ and y=k + r sinθ. The centre of x2 + y2 − 2x + 4y − 11 = 0 is (1,−2) and radius is √12 + (−2)2 − (−1) = 4 ⇒ Parametric equation isx=1 + 4 cosθ and y=−2 + 4 sinθ.

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