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For an equilateral triangle the centre is the origin and the length of altitude is $a .$ Then, the equation of the circumcircle is

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Important Questions on Conic Sections

EASY

Mathematics>Coordinate Geometry>Conic Sections>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>Conic Sections>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 :

HARD

Mathematics>Coordinate Geometry>Conic Sections>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>Conic Sections>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

HARD

Mathematics>Coordinate Geometry>Conic Sections>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>Conic Sections>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>Conic Sections>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 ?

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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

HARD

Mathematics>Coordinate Geometry>Conic Sections>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:

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

The equation of the circle with centre

(2, 2)

which passes through

(4, 5)

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

A circle with centre at

(3, 6)

passes through

(- 1, 1)

. Its equation is

HARD

Mathematics>Coordinate Geometry>Conic Sections>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>Conic Sections>Circle

The centre and radius of the circle

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

are

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

The equation of the circle concentric with the circle

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

and touching

Y

-axis

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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>Conic Sections>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

EASY

Mathematics>Coordinate Geometry>Conic Sections>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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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>Conic Sections>Circle

If a circle passing through the point

(- 1, 0)

touches

y

-axis at

(0, 2)

, then the

x

-intercept of the circle is

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

The circle passing through

(1, - 2)

and touching the axis of

x

(3, 0)

also passes through the point

For an equilateral triangle the centre is the origin and the length of altitude is a. Then, the equation of the circumcircle is

Important Questions on Conic Sections

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For an equilateral triangle the centre is the origin and the length of altitude is $a .$ Then, the equation of the circumcircle is