Question

For the circle $x^2+y^2-2x-4y+3=0$, the point $P(x,y)$:

• A. $(0,1)$ lies on the circle
• B. $(3,1)$ lies outside the circle
• C. $(1,3)$ lies inside the circle
• D. $(1,1)$ lies inside the circle

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $(0,1)$ lies on the circle
B $(3,1)$ lies outside the circle
C $(1,3)$ lies inside the circle
D $(1,1)$ lies inside the circle

Let $S=x^2+y^2-2x-4y+3=0$
(a) At point $(0,1)$
$S_1\equiv 0+1-0-4+3=0$, lies on the circle
(b) AT point $(3,1)$
$S_1\equiv 9+1-6-4+3=3>0$, lies outside the circle
(c) At point $(1,3)$
$S_1\equiv 1+9-2-12+3=-1<0$, lies inside the circle
(d) At point $(1,1)$
$S_1\equiv 1+1-2-4+3=-1<0$, lies inside the circle