HARD

Earn 100

Find the equation of the circle which touches both the axes and the coordinates of whose centre are $(h, k)$ .

Important Questions on Circle

MEDIUM

Mathematics>Coordinate Geometry>Circle>Equation of Circle

Let

C

be the circle with center at

(1, 1)

and radius

= 1

. If

T

is the circle centered at

(0, y)

, passing through the origin and touching the circle

C

externally, then the radius of

T

is equal to

HARD

Mathematics>Coordinate Geometry>Circle>Equation 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

HARD

Mathematics>Coordinate Geometry>Circle>Equation of Circle

The sides of right-angled triangle are integers. The length of one of the sides is

12

. The largest possible radius of the incircle of such a triangle is-

EASY

Mathematics>Coordinate Geometry>Circle>Equation 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 ……

HARD

Mathematics>Coordinate Geometry>Circle>Equation 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 :

HARD

Mathematics>Coordinate Geometry>Circle>Equation 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:

MEDIUM

Mathematics>Coordinate Geometry>Circle>Equation of Circle

The equation of the circle with centre

(2, 2)

which passes through

(4, 5)

EASY

Mathematics>Coordinate Geometry>Circle>Equation of Circle

The centre and radius of the circle

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

are

MEDIUM

Mathematics>Coordinate Geometry>Circle>Equation 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>Circle>Equation of Circle

If the incentre of an equilateral triangle is

(1, 1)

and the equation of its one side is

3 x + 4 y + 3 = 0

, then the equation of the circumcircle of this triangle is:

EASY

Mathematics>Coordinate Geometry>Circle>Equation 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>Circle>Equation 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>Circle>Equation 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

MEDIUM

Mathematics>Coordinate Geometry>Circle>Equation of Circle

A circle passes through

(- 2, 4)

and touches the

y -

axis at

(0, 2)

. Which one of the following equations can represent a diameter of this circle ?

EASY

Mathematics>Coordinate Geometry>Circle>Equation of Circle

A circle with centre at

(3, 6)

passes through

(- 1, 1)

. Its equation is

HARD

Mathematics>Coordinate Geometry>Circle>Equation of Circle

Let

P Q

be a diameter of the circle

x^{2} + y^{2} = 9

. If

α

and

β

are the lengths of the perpendiculars from

P

and

Q

on the straight line,

x + y = 2

respectively, then the maximum value of

α β

is _______

MEDIUM

Mathematics>Coordinate Geometry>Circle>Equation 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

HARD

Mathematics>Coordinate Geometry>Circle>Equation of Circle

If a circle passing through the point

(- 1, 0)

touches

y

-axis at

(0, 2)

, then the

x

-intercept of the circle is

HARD

Mathematics>Coordinate Geometry>Circle>Equation 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>Circle>Equation 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

Find the equation of the circle which touches both the axes and the coordinates of whose centre are (h, k).

Important Questions on Circle

Learn and Prepare for any exam you want !

Find the equation of the circle which touches both the axes and the coordinates of whose centre are $(h, k)$ .