Question

Find the position of the points $(1,2)$ and $(6,0)$ w.r.t the circle $x^2+y^2-4x+2y-11=0$

• A. $(1,2)$ lie outside the circle and the point $(6,0)$ lies inside the circle.
• B. $(1,2)$ and $(6,0)$ both lie inside the circle.
• C. $(1,2)$ and $(6,0)$ both lie outside the circle.
• D. $(1,2)$ lie inside the circle and the point $(6,0)$ lies outside the circle.

Answer 1

The correct option is D $(1,2)$ lie inside the circle and the point $(6,0)$ lies outside the circle.

Let $S(x,y)=x^2+y^2-4x+2y-11$
Now $S(1,2)=1+4-4+8-11=-2<0$
and $S(6,0)=36+0-24-11=1>0$
Hence point $(1,2)$ lie inside and point $(6,0)$ lies outside the given circle.