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Four distinct points $(2 k, 3 k), (1, 0), (0, 1)$ and $(0, 0)$ lie on a circle for

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all integral values of k

0 < k < l

k < 0

for two values of k

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detailed solution

Correct option is D

The equation of the circle passing through the point (1, 0), (0, 1) and (0, 0) is x2+y2−x−y=0This passes through (2k ,3k) 4k2+9k2−2k−3k=0⇒k=0,k=5/13

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Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for

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Four distinct points $(2 k, 3 k), (1, 0), (0, 1)$ and $(0, 0)$ lie on a circle for