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IMPORTANT

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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)

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Important Questions on Circle

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KVPY Aptitude Test - Stream SA

IMPORTANT

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

KVPY Aptitude Test - Stream SA

IMPORTANT

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})

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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 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

P

and

Q

meet at a point on the circle

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

then the equation of circle is

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

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

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

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

P

such that

O P = 6 \sqrt{2},

then the value of

c

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KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 21

The circle

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

cuts the line joining the points

A (1, 0)

and

B (3, 4)

in two points

P

and

Q .

Let

\frac{B P}{P A} = α

and

\frac{B Q}{Q A} = - β .

Then

α

and

β

are roots of the quadratic equation

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 11 - Circle>Exercise>Q 22

The equation of circumcircle of an equilateral triangle is

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

and one vertex of the triangle is

(1, 1),

the equation of incircle of the triangle is

If a circle of radius r is touching the lines x2-4xy+y2=0 in the first quadrant at points A and B, then area of triangle OAB is (O being the origin)

Important Questions on Circle

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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)