Question

circle drawn with origin as the centre passes through (13/2,0). The point which does not lie in the interior of the circle is:
a) (-3/4,1) b) (2,7/3) c) (5,-1/2) d) (-6,5/2)

Answer 1

Answer-
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)