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A circle passes through the points $A (1, 0), B (5, 0)$ and touches the $y$ -axis at $C (0, h)$ . If $∠ A C B$ is maximum then

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Important Questions on Circle

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 10

f (x, y) = x^{2} + y^{2} + 2 a x + 2 b y + c = 0

represents a circle. If

f (x, 0) = 0

has equal roots, each being

2

and

f (0, y) = 0

has

2

and

3

as it's roots, then centre of circle is

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

Consider a family of circle which are passing through the point

(- 1, 1)

and are tangent to

x

-axis. If

(h, k)

are the coordinates of the centre of the circles, then the set of values of

k

is given by the interval

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 12

If the conics whose equations are

S \equiv \sin^{2} θ x^{2} + 2 h x y + \cos^{2} θ y^{2} + 32 x + 16 y + 19 = 0, S^{'} \equiv \cos^{2} θ x^{2} + 2 h^{'} x y + \sin^{2} θ y^{2} + 16 x + 32 y + 19 = 0

intersects in four concyclic points then, (where

θ \in R

)

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 13

The range of values of

λ (λ > 0)

such that the angle

θ

between the pair of tangents drawn from

(λ, 0)

to the circle

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

lies in

(\frac{π}{2}, \frac{2 π}{3})

HARD

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 14

If a circle of radius

r

is touching the lines

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

in the first quadrant at points

A

and

B,

then area of triangle

O A B

is (

O

being the origin)

HARD

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 15

C_{1} : x^{2} + y^{2} = {(3 + 2 \sqrt{2})}^{2}

be a circle and

P A

and

P B

are pair of tangents on

C_{1},

where

P

is any point on the director circle of

C_{1}

, then the radius of smallest circle which touch

C_{1}

externally and also the two tangents

P A

and

P B

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 16

From a point

R (5, 8)

, two tangents

R P

and

R Q

are drawn to a given circle

S = 0

whose radius is

5

. If circumcentre of the triangle

P Q R

(2, 3)

, then the equation of circle

S = 0

HARD

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 17

The locus of the midpoints of the chords of the circle

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

which subtend a right angle at

(\frac{a}{2}, \frac{b}{2})

A circle passes through the points A1,0, B5,0 and touches the y-axis at C0,h. If ∠ACB is maximum then

Important Questions on Circle

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A circle passes through the points $A (1, 0), B (5, 0)$ and touches the $y$ -axis at $C (0, h)$ . If $∠ A C B$ is maximum then