Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 16

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The centre of a circle passing through the points $(0, 0), (1, 0)$ and touching the circle $x^{2} + y^{2} = 9$ is

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Important Questions on Circle

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 17

The equation(s) of the tangent at the point

(0, 0)

to the circle, making intercepts of length

2 a

and

2 b

units on the co-ordinate axes respectively, is (are)

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 18

Tangents are drawn to the circle

x^{2} + y^{2} = 50

from a point

P

lying on the

x

-axis. These tangents meet the

y

-axis at points

P_{1}

and

P_{2} .

Possible coordinates of

P

so that area of triangle

P P_{1} P_{2}

is minimum, is/are

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 19

The tangents drawn from the origin to the circle

x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0

are perpendicular if

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 20

The common chord of two intersecting circles

C_{1}

and

C_{2}

can be seen from their centres at the angles of

90 °

&

60 °

respectively. If the distance between their centres is equal to

\sqrt{3} + 1

then the radii of

C_{1}

and

C_{2}

are

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 21

A circle touches a straight line

f x + m y + n = 0

and cuts the circle

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

orthogonally. The locus of centres of such circles is

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 22

Equation

\frac{x - x_{1}}{\cos θ} = \frac{y - y_{1}}{\sin θ} = r

, may represents

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 23

If

r

represent the distance of a point from origin

& θ

is the angle made by line joining origin to that point from line

x

-axis, then

r = |\cos θ|

represents

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Beta Question Bank for Engineering: Mathematics>Chapter 17 - Circle>EXERCISE-2>Q 24

If the circle

C_{1} : x^{2} + y^{2} = 16

intersects another circle

C_{2}

of radius

5

in such a manner that the common chord is of maximum length

8

has a slope equal to

\frac{3}{4}

, then coordinates of centre of

C_{2}

are