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The number of rational point (S) (a point \( \Large \left(a,\ b \right) \) is called rational, if a and b both are rational number) on the circumference of a circle having centre \( \Large \left( \pi ,\ e\right) \) is:

A) at most one
B) at least two
C) exactly
D) infinite

Correct Answer:

A) at most one

Description for Correct answer:
If there are more than one rational point on the circumference of the circle

\( \Large x^{2}+y^{2}-2 \pi x - 2ey+c = 0 \)

[as \( \Large \left( \pi ,\ e\right) \) is the centre] then e will be a rational multiple of \( \Large \pi \), which is not possible. Thus the number of rational points on the circumference of the circle is at most one.

Part of solved Circles questions and answers : >> Elementary Mathematics >> Circles

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