Question

How are the points $(1,-3),(-2,-2)$ and $(0,-3)$ situated with respect to the circle $x^2+y^2+2x–y+3=0$

Answer 1

Given equation is $x^2+y^2+2x–y+3=0$

Let $A=(1,-3),B=(-2,-2)$ and $C=(0,-3)$

For point $A(1,-3),x^2+y^2+2x–y+3=1+9+2+3+3=18>0$

Hence point $A$ lies outside the circle

For point $B=(-2,-2),x^2+y^2+2x–y+3=4+4-4+2+3=9>0$

Hence point $B$ lies outside the circle

For point $C=(0,-3),x^2+y^2+2x–y+3=0+9+0+3+3=15>0$

Hence point $C$ lies outside the circle.