Parametric form of a circle and the point for a given parameter

1. A.
   $x=\frac{a}{2}+\frac{\sqrt{a^2+b^2}}{2}\cos\theta,\ y=\frac{b}{2}+\frac{\sqrt{a^2+b^2}}{2}\sin\theta$
2. B.
   $x=-\frac{a}{2}+\frac{\sqrt{a^2+b^2}}{4}\sin\theta,\ y=-\frac{b}{2}+\frac{\sqrt{a^2+b^2}}{4}\cos\theta$
3. C.
   $x=\frac{a}{2}+\frac{\sqrt{a^2+b^2}}{2}\sin\theta,\ y=\frac{b}{2}+\frac{\sqrt{a^2+b^2}}{2}\cos\theta$
4. D.
   $x=\frac{a}{2}+\frac{\sqrt{a^2+b^2}}{4}\cos\theta,\ y=\frac{b}{2}+\frac{\sqrt{a^2+b^2}}{4}\sin\theta$

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1. A.
   $x=-1+3\cos\theta,\;y=2+3\sin\theta$
2. B.
   $x=1+3\cos\theta,\;y=-2+3\sin\theta$
3. C.
   $x=-1+3\sin\theta,\;y=-2+3\cos\theta$
4. D.
   $x=1+3\sin\theta,\;y=-2+3\cos\theta$

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1. A.
   $x = 2 + 5\cos\theta, y = 3 + 5\sin\theta$
2. B.
   $x = -2 + 5\cos\theta, y = -3 + 5\sin\theta$
3. C.
   $x = 2 + 12\cos\theta, y = 3 + 12\sin\theta$
4. D.
   $x = 3 + 5\cos\theta, y = 2 + 5\sin\theta$

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1. A.
   $(1, 0)$
2. B.
   $(0, -2 + \sqrt{3})$
3. C.
   $(-1, -2)$
4. D.
   $(-\sqrt{3} + 1, -1)$

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