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The number of rational point(s) [a point...

The number of rational point(s) [a point (a, b) is called rational, if `aa n db` both are rational numbers] on the circumference of a circle having center `(pi,e)` is a)at most one b) at least two c)exactly two d) infinite

A

at most one

B

at least two

C

exactly two

D

inifinite

Text Solution

Verified by Experts

The correct Answer is:
1
If there are more than one rational points on the circumference of the circle `x^(2)+y^(2)-2pix-2ey+c=0` [ as `(pi,e)` is the center], then e will be a rational multiply of `pi`, which is not possible. Thus, the number of rational points on the circumference of the circle is atmost one.
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