A 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)
and how??
Answers
c) ( 5,-1/2).
The point (-6,5/2) does not lies in the interior of circle
Step-by-step explanation:
A circle drawn with origin as the centre passes through (13/2,0)
(x - h)² + (y - k)² = r²
h & k = 0 as center is at origin
=> x² + y² = r²
Passes through 13/2 , 0
=> (13/2)² + 0² = r²
=> r² = (13/2)²
=> x² + y² = (13/2)²
x² + y² < (13/2)² lies inside circle
The point x² + y² ≥ (13/2)² does not lies in the interior of circle
option given are:
a) (-3/4,1) b) (2,7/3) c) (5,-1/2) d) (-6,5/2)
-3/4,1 => x² + y² = 25/16 = (5/4)² < (13/2)²
(2,7/3) => x² + y² = 85/9 < (13/2)²
(5,-1/2) => x² + y² = 101/4 < (13/2)²
(-6,5/2) => x² + y² = 169/4 = (13/2)²
hence (-6,5/2) does not lies in the interior of circle
it lies on circle
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