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  • The number of rational point(s) (a point (a, b) is called rational, if a and b both are rational numbers) on the circumsference of a circle having center <img alt="\mathrm{(\pi, e)}" src="https://e

The number of rational point(s) (a point (a, b) is called rational, if a and b both are rational numbers) on the circumsference of a circle having center \mathrm{(\pi, e)} is
 

Option: 1

at most one

 


Option: 2

at least two
 


Option: 3

exactly two
 


Option: 4

infinite


Answers (1)

If there are more than one rational points on the circunference of the circle \mathrm{x^2+y^2-2 \pi x -2 ey +c=0, (as (\pi, e)} \mathrm{\text{is the centre)}}, then \mathrm{e} will be a rational multiple of \mathrm{\pi}, which is not possible. Thus the number of rational points on the circumference of the circle is at most one.

Hence option 1 is correct.

Posted by

Kshitij

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