# Discuss the position of the points (2,3) and(1,3) with respect to circle $x^2+y^2-4x+2y-11=0$?

$\begin{array}{1 1}(a)\;\text{inside the circle}\\(b)\;\text{outside the circle}\\(c)\;\text{centre of the circle}\\(d)\;\text{None of these}\end{array}$

$s=x^2+y^2-4x+2y-11=0$ for the point (1,3)
$1^2+3^2-4(1)+2(3)-11 > 0$
So (1,3) lie outside the circle
Now for (2,3)
$(2)^2+(3)^2-4(2)+2(3)-11>0$
So (2,3) lie outside the circle.
Hence (b) is the correct answer.