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

Question

If x = 2 + 3 cos θ and y = 1 + 3 sin θ represent a circle then the centre and radius is (A) (2,1), 9 (B) (2,1), 3 (C) (1,2), (1/3) (D) (-2,-1), 3

Tardigrade Admin · Accepted Answer

We have, x=2+3 cos θ and y=1-3 sin θ ⇒ (x-2)=3 cos θ dots(i) and (y-1)=-3 sin θ dots(ii) On squaring and adding Eqs. (i) and (ii), we get (x-2)2+(y-1)2=9 ∴ Centre =(2,1) and radius =3

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

$(2, 1), 9$

$(2, 1), 3$

$(1, 2), \frac{1}{3}$

$(- 2, - 1), 3$

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

Q. If x=2+3cosθ and y=1+3sinθ represent a circle then the centre and radius is

(2,1),9

(2,1),3

(1,2),31​

(−2,−1),3