Question

Which of the following point lie inside the circle $x^2+y^2-2x+3y-11=0$

• A. (2, 3)
• B. (1, 1)
• C. (-1, 2)
• D. (3, 2)

Answer 1

The correct option is B

(1, 1)

To find if a point lies inside or outside a given circle, we will find S1 by substituting the given point in the equation of the circle and check its sign.

(a) (2, 3)

$S_1\equiv 2^2+3^2-2\times 2+3\times 3-11=7$

$S_1>0\Rightarrow$outside

(b) (1, 1)

$S_1\equiv 1+1-2+3-11=-8$

$S_1<0\Rightarrow$ inside

(c) (-1, 2)

$S_1\equiv 1+4+2+6-11=2$

$S_1>0\Rightarrow$ outside

(d) (3, 2)

$S_1\equiv 3^2+2^2-2\times 3+3\times 2-11=2$

$S_1>0\Rightarrow$ outside

$\Rightarrow$ 3 points lie outside the given circle. Alternate method: we can find the distance of these points from the centre and compare it with the radius. If it is greater than radius, the point will lie outside the circle.