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  • Four distinct points <img alt="(2 \mathrm{k}, 3 \mathrm{k}),(1,0),(0,1)" src="https://entrancecorner.oncodecogs.com/gif.latex?%282%20%5Cmathrm%7Bk%7D%2C%203%20%5Cmathrm%7Bk%7D%29%2C%281%2C0%29%2C%2

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

Option: 1

all integral values of \mathrm{k}


Option: 2

0<\mathrm{k}<1


Option: 3

\mathrm{k}<0


Option: 4

for two values of \mathrm{k}


Answers (1)

best_answer

The equation of the circle passing through the point (1,0),(0,1) $ and $(0,0) is \mathrm{x^2} +\mathrm{y^2} -\mathrm{x}-\mathrm{y}=0

This passes through (2 \mathrm{k}, 3 \mathrm{k}), therefore
4 \mathrm{k^2} +9 \mathrm{k^2} -2 \mathrm{k}-3 \mathrm{k}=0 \quad \mathrm{k}=0, \mathrm{k}=5 / 13

Posted by

Suraj Bhandari

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