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  • The maximum number of points with rational coordinates, on a circle whose centre is <img alt="\mathrm{(\sqrt{5}, 0)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28%5Csqrt%7B5

The maximum number of points with rational coordinates, on a circle whose centre is \mathrm{(\sqrt{5}, 0)}, is
 

Option: 1

one


 


Option: 2

two
 


Option: 3

three


Option: 4

infinite


Answers (1)

best_answer

The equation of the circle with radius \mathrm{r} is \mathrm{x^2+y^2-2 \sqrt{5}=r^2-5\: If\: r^2-5} is rational, then one possible solution is \mathrm{x=0}
\mathrm{\Rightarrow y= \pm \sqrt{r^2-5}. \: If\: r^2-5} is irrational, then the rational part are given by \mathrm{x^2+y^2 =0}
\mathrm{\Rightarrow x=0, y=0,} which is not possible

Hence maximum number of rational part possible is 2 .

Hence option 2 is correct.

Posted by

Riya

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