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  4. If x = 2 + 3 cos θ and y = 1 + 3 sin θ represent a circle then the centre and radius is

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Q. If $x = 2 + 3 \, \cos\, \theta$ and $y = 1 + 3\, \sin \, \theta$ represent a circle then the centre and radius is

KCETKCET 2016Conic Sections

Solution:

We have, $x=2+3 \,\cos\, \theta$
and $y=1-3 \,\sin\, \theta$
$\Rightarrow (x-2)=3 \,\cos \,\theta\dots$(i)
and $(y-1)=-3\, \sin\, \theta \dots$(ii)
On squaring and adding Eqs. (i) and (ii), we get
$(x-2)^{2}+(y-1)^{2}=9$
$\therefore $ Centre $=(2,1)$ and radius $=3$