Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 19

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If the centroid of an equilateral triangle is $(1, 1)$ and its one vertex is $(- 1, 2)$ , then the equation of its circumcircle is

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Important Questions on Conic Sections

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 20

If the circles

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

and

x^{2} + y^{2} + 8 y + c = 0

touch each other, then

c

is equal to

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 21

The equation of a circle with radius

5

and touching both the coordinate axes is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 22

Find the equation of the circle which passes through the points

(2, 3)

and

(4, 5)

) and the centre lies on the straight line

y - 4 x + 3 = 0 .

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 23

The parametric equations of the circle

x^{2} + y^{2} + mx + my = 0

are

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 24

The centre of the circle inscribed in a square formed by the lines

x^{2} - 8 x + 12 = 0

and

y^{2} - 14 y + 45 = 0

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 25

The length of the diameter of the circle which touches the

x -

axis at the point

(1, 0)

and passes through the point

(2, 3)

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 26

The radius of the circle passing through the point

(6, 2)

two of whose diameter are

x + y = 6

and

x + 2 y = 4

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 10 - Conic Sections>Exercise>Q 27

Let

C

be the circle with centre 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