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Question

Which of the following point lie inside the circle x2+y2−2x+3y−11=0


A

(2, 3)

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B

(1, 1)

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C

(-1, 2)

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D

(3, 2)

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Solution

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)

S122+322×2+3×311=7

S1>0outside

(b) (1, 1)

S11+12+311=8

S1<0 inside

(c) (-1, 2)

S11+4+2+611=2

S1>0 outside

(d) (3, 2)

S132+222×3+3×211=2

S1>0 outside

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.


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