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Given the equation of the circle is x^2 + y^2 = 5^2. How many points

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Given the equation of the circle is x^2 + y^2 = 5^2. How many points  [#permalink]

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New post Updated on: 21 Jul 2018, 05:18
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Given the equation of the circle is x^2 + y^2 = 5^2 . How many points on the circumference have both x and y coordinates integers ?

12

Originally posted by Arun1994 on 21 Jul 2018, 03:17.
Last edited by Arun1994 on 21 Jul 2018, 05:18, edited 1 time in total.
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Re: Given the equation of the circle is x^2 + y^2 = 5^2. How many points  [#permalink]

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New post Updated on: 21 Jul 2018, 05:09
Circle Equation : \(x^2 + y^2 = 5^2\)

This is the equation of circle with Center (0,0) and radius = 5.

So we have 4 points on the circumference that are integers --> \((5,0) , (-5,0) , (0,5) , (0,-5)\)

For any point (a,b) on the circumference, distance from center = radius

\((x-a)^2 + (y-b) = 5^2\)

Substituting (x,y) =(0,0) and the equation becomes

\(a^2 + b^2 = 5^2\)

Integer Value pairs satisfying the above equation are (a,b)==> \((4,3) , (-4,3), (4,-3) , (-4, -3), (3,4), (-3,4), (3,-4), (-3,-4)\)

Total number of points = 4+8= \(12\) points

Originally posted by siddharthabingi on 21 Jul 2018, 03:38.
Last edited by siddharthabingi on 21 Jul 2018, 05:09, edited 1 time in total.
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Re: Given the equation of the circle is x^2 + y^2 = 5^2. How many points  [#permalink]

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New post 21 Jul 2018, 03:49
siddharthabingi wrote:
Circle Equation : \(x^2 + y^2 = 5^2\)

This is the equation of circle with Center (0,0) and radius = 5.

So we have 4 points on the circumference that are integers --> \((5,0) , (-5,0) , (0,5) , (0,-5)\)

For any point (a,b) on the circumference, distance from center = radius

\((x-a)^2 + (y-b) = 5^2\)

Substituting (x,y) =(0,0) and the equation becomes

\(a^2 + b^2 = 5^2\)

Integer Value pairs satisfying the above equation are (a,b)==> \((4,3) , (-4,3), (4,-3) , (-4, -3)\)

Total number of points = 4+4 = \(8\) points


Hi siddharthabingi,

What about (3,4),(3,-4),(-3,4),(-3,-4) ?
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Re: Given the equation of the circle is x^2 + y^2 = 5^2. How many points  [#permalink]

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New post 21 Jul 2018, 03:49
siddharthabingi wrote:
Circle Equation : \(x^2 + y^2 = 5^2\)

This is the equation of circle with Center (0,0) and radius = 5.

So we have 4 points on the circumference that are integers --> \((5,0) , (-5,0) , (0,5) , (0,-5)\)

For any point (a,b) on the circumference, distance from center = radius

\((x-a)^2 + (y-b) = 5^2\)

Substituting (x,y) =(0,0) and the equation becomes

\(a^2 + b^2 = 5^2\)

Integer Value pairs satisfying the above equation are (a,b)==> \((4,3) , (-4,3), (4,-3) , (-4, -3)\)

Total number of points = 4+4 = \(8\) points


Hi siddharthabingi,

Shouldn't it be 12 Points. Not sure, if I am missing anything.

\((5,0) (0,5) (0,-5) (-5, 0) (3,4) (4,3) (-3,-4) (-4,-3) (-3,4) (4,-3) (3,-4) (-4,3)\) \(= 12 Points.\)
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Re: Given the equation of the circle is x^2 + y^2 = 5^2. How many points  [#permalink]

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New post 21 Jul 2018, 03:52
rahul16singh28 wrote:
siddharthabingi wrote:
Circle Equation : \(x^2 + y^2 = 5^2\)

This is the equation of circle with Center (0,0) and radius = 5.

So we have 4 points on the circumference that are integers --> \((5,0) , (-5,0) , (0,5) , (0,-5)\)

For any point (a,b) on the circumference, distance from center = radius

\((x-a)^2 + (y-b) = 5^2\)

Substituting (x,y) =(0,0) and the equation becomes

\(a^2 + b^2 = 5^2\)

Integer Value pairs satisfying the above equation are (a,b)==> \((4,3) , (-4,3), (4,-3) , (-4, -3)\)

Total number of points = 4+4 = \(8\) points


Hi siddharthabingi,

Shouldn't it be 12 Points. Not sure, if I am missing anything.

\((5,0) (0,5) (0,-5) (-5, 0) (3,4) (4,3) (-3,-4) (-4,-3) (-3,4) (4,-3) (3,-4) (-4,3)\) \(= 12 Points.\)
No you aren't missing out anything. This should be right.

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Re: Given the equation of the circle is x^2 + y^2 = 5^2. How many points  [#permalink]

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New post 21 Jul 2018, 05:07
rahul16singh28 wrote:
siddharthabingi wrote:
Circle Equation : \(x^2 + y^2 = 5^2\)

This is the equation of circle with Center (0,0) and radius = 5.

So we have 4 points on the circumference that are integers --> \((5,0) , (-5,0) , (0,5) , (0,-5)\)

For any point (a,b) on the circumference, distance from center = radius

\((x-a)^2 + (y-b) = 5^2\)

Substituting (x,y) =(0,0) and the equation becomes

\(a^2 + b^2 = 5^2\)

Integer Value pairs satisfying the above equation are (a,b)==> \((4,3) , (-4,3), (4,-3) , (-4, -3)\)

Total number of points = 4+4 = \(8\) points


Hi siddharthabingi,

Shouldn't it be 12 Points. Not sure, if I am missing anything.

\((5,0) (0,5) (0,-5) (-5, 0) (3,4) (4,3) (-3,-4) (-4,-3) (-3,4) (4,-3) (3,-4) (-4,3)\) \(= 12 Points.\)



Thank you. I missed that part. I will correct it. :D
Re: Given the equation of the circle is x^2 + y^2 = 5^2. How many points &nbs [#permalink] 21 Jul 2018, 05:07
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