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

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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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Important Questions on Circle

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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})

is

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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

If

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

is

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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

is

(2, 3)

, then the equation of circle

S = 0

is

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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})

is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 18

A tangent at a point on the circle

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

intersects a concentric circle

C

at two points

P

and

Q

. The tangents to the circle

X

at

P

and

Q

meet at a point on the circle

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

then the equation of circle is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 19

The chord of contact of tangents from a point

P

to a circle passes through

Q

. If

l_{1}

and

l_{2}

are the lengths of the tangents from

P

and

Q

to the circle, then

P Q

is equal to

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 20

If the circle

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

is touched by

y = x

at

P

such that

O P = 6 \sqrt{2},

then the value of

c

is