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

Options

A. at most one
B. at least two
C. exactly two
D. inifinite

Answer

1

Explanation

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.