MEDIUM

Earn 100

The distinct points $A (0, 0), B (0, 1), C (1, 0)$ and $D (2 a, 3 a)$ are concyclic, then

56.94% studentsanswered this correctly

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 distinct points A0, 0, B0, 1, C(1, 0) and D(2a, 3a) are concyclic, then

Important Questions on Circles

Learn and Prepare for any exam you want !

The distinct points $A (0, 0), B (0, 1), C (1, 0)$ and $D (2 a, 3 a)$ are concyclic, then