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The centres of three circles $x^{2} + y^{2} = 1, x^{2} + y^{2} + 6 x - 2 y = 1, x^{2} + y^{2} - 12 x + 4 y = 1$ are

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Important Questions on Circles

MEDIUM

Mathematics>Coordinate Geometry>Circles>Basics of Circle

If one of the diameters of the circle, given by the equation,

x^{2} + y^{2} - 4 x + 6 y - 12 = 0,

is a chord of a circle

S,

whose centre is at

(- 3, 2),

then the radius of

S

HARD

Mathematics>Coordinate Geometry>Circles>Basics of Circle

A circle touching the

x -

axis at

(3, 0)

and making an intercept of length

8

on the

y -

axis passes through the point:

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The intercept on the line

y = x

by the circle

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

A B

. The equation of the circle with

A B

as a diameter is ……

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The centre and radius of the circle

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

are

HARD

Mathematics>Coordinate Geometry>Circles>Basics of Circle

A circle passes through the points

(2, 3)

and

(4, 5)

. If its centre lies on the line

y - 4 x + 3 = 0

, then its radius is equal to :

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

A circle with centre at

(3, 6)

passes through

(- 1, 1)

. Its equation is

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The equation of the circle concentric with the circle

x^{2} + y^{2} - 6 x - 4 y - 12 = 0

and touching

Y

-axis

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

If the coordinates of one end of a diameter of the circle

x^{2} + y^{2} - 8 x - 4 y + c = 0

are

(- 3, 2)

, then the coordinates at the other end are

MEDIUM

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The circle passing through

(1, - 2)

and touching the axis of

x

(3, 0)

also passes through the point

HARD

Mathematics>Coordinate Geometry>Circles>Basics of Circle

In a circle of radius

17 c m,

two parallel chords are drawn on opposite side of a diameter. The distance between the chords is

23 c m .

If the length of one chord is

16 c m,

then the length of the other chord is

MEDIUM

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The equation of the circle whose radius is

\sqrt{7}

and concentric with the circle

x^{2} + y^{2} - 8 x + 6 y - 11 = 0

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

Let

C_{1}

and

C_{2}

be the centres of the circles

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

and

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

respectively. If

P

and

Q

are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral

P C_{1} Q C_{2}

is :

MEDIUM

Mathematics>Coordinate Geometry>Circles>Basics of Circle

A circle has radius

3

and its centre lies on the line

y = x - 1

. The equation of the circle, if it passes through

(7, 3)

, is

MEDIUM

Mathematics>Coordinate Geometry>Circles>Basics of Circle

If the tangent at

(1, 7)

to the curve

x^{2} = y - 6

touches the circle

x^{2} + y^{2} + 16 x + 12 y + c = 0,

then the value of

c

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

If the lines

3 x - 4 y + 4 = 0

and

6 x - 8 y - 7 = 0

are tangents to a circle, then radius of the circle is

HARD

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The radius of the circle

2 x^{2} + 2 y^{2} - 3 x + 2 y - 1 = 0

is _________ units.

HARD

Mathematics>Coordinate Geometry>Circles>Basics of Circle

If two distinct chords drawn from the point

(p, q)

on the circle

x^{2} + y^{2} = p x + q y

(where

p q \neq 0

) are bisected by the

X

-axis, then

MEDIUM

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The equation of the circle with centre

(2, 2)

which passes through

(4, 5)

HARD

Mathematics>Coordinate Geometry>Circles>Basics of Circle

If the area of an equilateral triangle inscribed in the circle

x^{2} + y^{2} + 10 x + 12 y + c = 0

27 \sqrt{3} sq . units,

then

c

is equal to:

EASY

Mathematics>Coordinate Geometry>Circles>Basics of Circle

The sides of a rectangle are given by

x = \pm a

and

y = \pm b

. Then equation of the circle passing through the vertices of the rectangle is

The centres of three circles x2+y2=1, x2+y2+6x-2y=1, x2+y2-12x+4y=1 are

Important Questions on Circles

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The centres of three circles $x^{2} + y^{2} = 1, x^{2} + y^{2} + 6 x - 2 y = 1, x^{2} + y^{2} - 12 x + 4 y = 1$ are