Find the parametric equation of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$

$x = - 2 + 4 c o s θ a n d y = + 4 + 4 c o s θ$

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$x = - 2 + 4 c o s θ a n d y = + 4 + 4 c o s θ$

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$x = - 1 + 4 c o s θ a n d y = + 2 + 4 s i n θ$

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$x = 1 + 4 c o s θ a n d y = - 2 + 4 s i n θ$

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Solution

The correct option is D
$x = 1 + 4 c o s θ a n d y = - 2 + 4 s i n θ$

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 $x = h + r c o s θ a n d y = k + r s i n θ$ .
The centre of $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ is $(1, - 2)$ and radius is $\sqrt{1^{2} + (- 2)^{2} - (- 1)} = 4$

$\Rightarrow$ Parametric equation is $x = 1 + 4 c o s θ a n d y = - 2 + 4 s i n θ$ .

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

Find the parametric equation of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$