Rational point's

How Many Rational Point's are enclosed by an circle Having centre $e$ , $pi$ ?

Please Help

Thanks!

#Algebra #Help

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

What is the radius of the circle?

Sudeep Salgia - 6 years, 5 months ago

Actually This question was Given To me By My Freind And He is So cruel and Doesn't Give any Information for radius .

Karan Shekhawat - 6 years, 5 months ago

If the question means asks to find the number of rational points ( assuming it means points whose coordinates are rational numbers ) " enclosed " by the circle i.e., the union of set of points within the circle and on the circle it would strongly depend upon radius and I feel there would not be any nice looking formula for the same. If the questions demands to find the points lying "on" the circle then Ronak's argument seems quite valid.

Sudeep Salgia - 6 years, 5 months ago

@Sudeep Salgia – yeah Thanks a ton , Now I got it !

Karan Shekhawat - 6 years, 5 months ago

If the radius of the circle not given then there is at most one rational point, since your arbitarily choose a point like (3,5) and hence decide the radius of the circle but then you will not get another rational point.

Ronak Agarwal - 6 years, 5 months ago

Could You Please Explain More , It sound's Interesting !

And If Radius is fixed Then ? @Ronak Agarwal

Karan Shekhawat - 6 years, 5 months ago

My argument works for only the points lying on the circle. For finding the number of points enclosed by the circle it is impossible to find it without knowing the radius.

Ronak Agarwal - 6 years, 5 months ago

@Ronak Agarwal – Yes I understand , My cruel friend tell me Poorly , Instead of This He should ask number of points Lies on Circle , which is 1 as You Explained betterly ! And Thanks for Replying :)

Karan Shekhawat - 6 years, 5 months ago

@Karan Shekhawat – Is your friend enrolled in fiitjee , cause this question recently appeared in AITS PART-TEST 2 @KARAN SHEKHAWAT

Ronak Agarwal - 6 years, 5 months ago

@Ronak Agarwal – I don't know , May be He is ! Hey when did Fiitjee AITS starded ? Can I enroll in it now ? I want to give full length test of AITS . Can You Please Tell me Procedure and Time table of Exams ?

Also What rank did You get in it ?, I'am just curious to know !

Karan Shekhawat - 6 years, 5 months ago

@Karan Shekhawat – Part Test -1 All India Rank-4

Part Test-2 All India Rank-34

Part Test-3 All India Rank-Yet to be known

Ronak Agarwal - 6 years, 5 months ago

@Ronak Agarwal – wow ! That's Great ! Can You Please Tell me procedure also ? @Ronak Agarwal
Also It is not good to ask But still , How much % wise You Got in AITS ? Please reply Ronak .

Karan Shekhawat - 6 years, 5 months ago

@Karan Shekhawat – Check this Fiitjee AITS

@KARAN SHEKHAWAT

Ronak Agarwal - 6 years, 5 months ago

@Karan Shekhawat – AITS-1 Percentage =63.33 %

AITS-2 Percentage =56.11 %

AITS-3 Percentage = Yet to be known.

Ronak Agarwal - 6 years, 5 months ago

@Ronak Agarwal – Thanks ! Is All paper are of 360 marks ? i think difficulty level of these paper are High .

Karan Shekhawat - 6 years, 5 months ago

@Karan Shekhawat – Yes, actually there are two papers paper 1, paper 2 and yes they are quite tough.

Ronak Agarwal - 6 years, 5 months ago

@Ronak Agarwal – Congratulations!! Nice work!!

Sudeep Salgia - 6 years, 5 months ago

@Deepanshu Gupta @megh choksi @Ronak Agarwal @Mvs Saketh @Sudeep Salgia @Karthik Kannan @jatin yadav @Krishna Sharma

Karan Shekhawat - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$