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The equation of the circle touching the $x$ -axis at $(5, 0)$ and the line $y = 10$ is

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Important Questions on Circles

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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 ……

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

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:

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Mathematics>Coordinate Geometry>Circles>Basics of Circle

In the following sentence, a blank space with four options is given. Select whichever preposition or determiner you consider the most appropriate for the blank space.

These are the good rules to live _____.

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Mathematics>Coordinate Geometry>Circles>Basics of Circle

Two sentences are given below and you are required to find the correct sentence which combines both the sentences.

Which is the correct combination of the given two sentences?

He is too tired. He could not stand.

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

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Mathematics>Coordinate Geometry>Circles>Basics of Circle

The equation of the circle with centre

(2, 2)

which passes through

(4, 5)

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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

MEDIUM

Mathematics>Coordinate Geometry>Circles>Basics of Circle

Directions: Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.

Every rash driver becomes a ____ killer.

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:

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

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

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Mathematics>Coordinate Geometry>Circles>Basics of Circle

A circle with centre at

(3, 6)

passes through

(- 1, 1)

. Its equation is

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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

The centre and radius of the circle

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

are

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

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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

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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

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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 :

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 :

The equation of the circle touching the x-axis at 5,0 and the line y=10 is

Important Questions on Circles

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The equation of the circle touching the $x$ -axis at $(5, 0)$ and the line $y = 10$ is