Question

15. Does the point (-2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?​

Answer 1

Answer :

Inside

Note :

• The equation of circle with center (0,0) is given as : x² + y² = r² , where r = radius of the circle.

• If the point (a,b) lies on the circle , then it must satisfy the equation of the circle , ie. a² + b² = r² .

• If the point (a,b) lies inside the circle , then a² + b² < r² .

• If the point (a,b) lies outside the circle , then a² + b² > r² .

Solution :

Here ,

The given equation of circle is :

x² + y² = 25 -------(1)

Also ,

The given point is (-2.5 , 3.5) .

Now ,

Putting x = -2.5 and y = 3.5 in the RHS of eq-(1) , we get ;

x² + y² = (-2.5)² + (3.5)²

= 6.25 + 12.25

= 18.5

< 25

Clearly ,

(-2.5)² + (3.5)² < 25 , thus the point (-2.5 , 3.5) lies inside the circle .