Question

Does the point (–2.5, 3.5) lie inside, outside or on the circle x 2 + y 2 = 25?

Answer 1

Given the equation of the circle as x 2 + y 2 =25 .

The equation of the required circle is given by,

( x−h ) 2 + ( y−k ) 2 = r 2 (1)

Where h and k denotes the center of the circle and r denotes the radius of the circle.

Give equation can be written as,

( x−0 ) 2 + ( y−0 ) 2 = 5 2 (2)

By comparing equation (1) and (2) we get,

h=0,k=0 and r=5

The distance between two points ( x 1 , x 2 ) and ( y 1 , y 2 ) is given by the formula,

( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2

The distance between the point ( −2.5,3.5 ) and center ( 0,0 ) is given by,

= ( 0−( −2.5 ) ) 2 + ( 0−3.5 ) 2 = 6.25+12.25 = 18.5 =4.3(approx.)<5

Thus the distance between the point ( −2.5,3.5 ) and the center ( 0,0 ) is less than 5 that less than the radius. Hence the point ( −2.5,3.5 ) lies inside the circle.