Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 25

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A circle with radius $|a|$ and centre on $y$ -axis slides along it and a variable lines through $(a, 0)$ cuts the circle at points $P$ and $Q .$ The region in which the point of intersection of tangents to the circle at points $P$ and $Q$ lies is represented by

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Important Questions on Circle

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 26

The centres of a set of circle, each of radius

3,

lies on the circle

x^{2} + y^{2} = 25,

The locus of any point in the set is

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 27

The coordinates of two points

P

and

Q

are

(x_{1}, y_{1})

and

(x_{2}, y_{2})

and

O

is the origin. If circles be described on

O P

and

O Q

as diameters, then the length of their common chord is

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 28

If the circumference of the circle

x^{2} + y^{2} + 8 x + 8 y - b = 0

is bisected by the circle

x^{2} + y^{2} - 2 x + 4 y + a = 0,

then

a + b

equals to

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KVPY Aptitude Test - Stream SA

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 29

The equation of the circle passing through the point of intersection of the circle

x^{2} + y^{2} = 4

and the line

2 x + y = 1

and having minimum possible radius is