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Two parallel chords of a circle of radius $2$ are at a distance $\sqrt{3} + 1$ apart. If the chords subtend the angles $\frac{π}{k}$ and $\frac{2 π}{k}$ at the center, where $k > 0$ , then the value of $[k]$ is: (Note: $[k]$ denotes the largest integer less than or equal to $k$ )

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Important Questions on Conic Sections

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:

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

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

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>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

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 ……

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

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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

The equation of the circle with centre

(2, 2)

which passes through

(4, 5)

HARD

Mathematics>Coordinate Geometry>Conic Sections>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-

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

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

A circle with centre at

(3, 6)

passes through

(- 1, 1)

. Its equation is

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

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

The centre and radius of the circle

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

are

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

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>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

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 :

Two parallel chords of a circle of radius 2 are at a distance 3+1 apart. If the chords subtend the angles πk and 2πk at the center, where k>0, then the value of k is: (Note: k denotes the largest integer less than or equal to k)

Important Questions on Conic Sections

Learn and Prepare for any exam you want !

Two parallel chords of a circle of radius $2$ are at a distance $\sqrt{3} + 1$ apart. If the chords subtend the angles $\frac{π}{k}$ and $\frac{2 π}{k}$ at the center, where $k > 0$ , then the value of $[k]$ is: (Note: $[k]$ denotes the largest integer less than or equal to $k$ )