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Problem 20

The number of points with integral co-ordinates that are interior to the circle \(x^{2}+y^{2}=16\) is : (a) 43 (b) 45 (c) 47 (d) 49

Expert verified

The number of points with integral coordinates that are interior to the circle \(x^{2}+y^{2}=16\) is 145.

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Chapter 1

For what values of \(l\) and \(m\), circle \(5\left(x^{2}+y^{2}\right)+b y-m=0\) belongs to the co-axial system determined by the circles $x^{2}+y^{2}+2 x+4 y-6=0\( and \)2\left(x^{2}+y^{2}\right)-x=0 ?$

Chapter 1

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Chapter 1

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Chapter 1

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Chapter 1

An equation of a circle touching the axes of co-ordinates and the line $x \cos \alpha+y \sin \alpha=2$ can be : (a) \(x^{2}+y^{2}-2 g x-2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha+\sin \alpha+1)$ (b) \(x^{2}+y^{2}-2 g x-2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha+\sin \alpha-1)$ (c) \(x^{2}+y^{2}-2 g x+2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha-\sin \alpha+1)$ (d) \(x^{2}+y^{2}-2 g x+2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha-\sin \alpha-1)$

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