Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 14

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Earn 100

STATEMENT- $1$ : If three circles which are such that their centres are non-collinear, then exactly one circle exists which cuts the three circles orthogonally.

STATEMENT- $2$ : Radical axis for two intersecting circles is the common chord.

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Important Questions on Circle

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 15

The centre of family of circles cutting the family of circles

x^{2} + y^{2} + 4 x (λ - \frac{3}{2}) + 3 y (λ - \frac{4}{3}) - 6 (λ + 2) = 0

orthogonally, lies on

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 21

Let

x & y

be the real numbers satisfying the equation

x^{2} - 4 x + y^{2} + 3 = 0

. If the maximum and minimum values of

x^{2} + y^{2}

are

M & m

, respectively, then find the numerical value of

(M + m)

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 27

Let

A

be the centre of the circle

x^{2} + y^{2} - 2 x - 4 y - 20 = 0 .

Suppose that the tangents at the points

B (1, 7) & D (4, - 2)

on the circle meet at the point

C .

Find the area of the quadrilateral

A B C D .

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 30

The circumference of the circle

x^{2} + y^{2} - 2 x + 8 y - q = 0

is bisected by the circle

x^{2} + y^{2} + 4 x + 12 y + p = 0,

then find

p + q

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 32

The equation of circles passing through

(3, - 6)

touching both the axes is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 34

The centre of a circle passing through the points

(0, 0), (1, 0) &

touching the circle

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

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 35

The equation of the circle which touches both the axes and the line

\frac{x}{3} + \frac{y}{4} = 1

and lies in the first quadrant is

(x - c)^{2} + (y - c)^{2} = c^{2}

where

c

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 36

Find the equations of straight lines which pass through the intersection of the lines

x - 2 y - 5 = 0

and

7 x + y = 50

&

divide the circumference of the circle

x^{2} + y^{2} = 100

into two arcs whose lengths are in the ratio

2 : 1

.