Question

A circle drawn with origin as the centre passes through( 5/2,0).does the point (5/2,5/2) lies exterior or interir?

Answer 1

Given, centre of circle is (0, 0) And circle passes through the point (13/2, 0). Radius of circle = Distance between (0, 0) and (13/2,0)
Radius of circle = √(13/2-0)²+ (0-0)²
= 13/2 = 6.5
(a) Distance between (0, 0) and (-3/4,1)
√(-3/4-0)²+(1-0)²
= 5/4 = 1.25 which is less than 6.5
So, the point P (-3/4,1) lies interior to the circle.

(b) Distance between (0, 0) and (2, 7/3)
√(2-0)²+(7/3-0)²
= 9.22/3 = 3.1 which is less than 6.5
Hence, the point (2, 7/3) lies inside the circle.

(c) Distance between (0, 0) and (5,-1/2)
√(5-0)²+(-1/2-0)²
= 10.04/2 = 5.02 which is less than 6.5.
Hence, the point (5,-1/2) lies inside the circle.
(d) Distance between (0, 0) and (-6,5/2)
√(-6-0)²+(5/2-0)²
= 13/2 = 6.5 which is equal to 6.5.
Hence, the point (-6,5/2) lies on the circle.

Answer=(d) = (-6,5/2)