Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 10

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The centre of a circle which is orthogonal to the circles $C_{1} : x^{2} + y^{2} = 25$ and $C_{2} : (x - 7)^{2} + (y - 5)^{2} = 4$ and which has the least radius is:

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Important Questions on Circle

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 11

The equation

x^{2} + y^{2} = ||2 x - 2| + 2 |y - 1||

represents :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 12

The points

(4, - 2)

and

(3, b)

are conjugate with respect to the circle

x^{2} + y^{2} = 24

, if

b =

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 13

A ray of light incident at the point

(- 2, - 1)

gets reflected from the tangent at

(0, - 1)

to the circle

x^{2} + y^{2} = 1

, such that the reflected ray touches the circle. Then, the equation of the line along the incident ray is

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 14

The circle

x^{2} + y^{2} + 4 x - 6 y + 9 = 0

undergoes the following transformation

3 f (x, y) - f (x + 1, y) + f (x, y + 1) = 0

then the ratio of areas of the new circle to original circle is :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 15

The equation of the image of the circle

{(x - 3)}^{2} + {(y - 2)}^{2} = 1

by the mirror

x + y = 19

is

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 16

The circle

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

cuts the line joining the points

A (1, 0)

and

B (3, 4)

in two points

P

and

Q .

Let

\frac{B P}{P A} = α

and

\frac{B Q}{Q A} = - β .

Then

α

and

β

are roots of the quadratic equation

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 17

The area bounded by the circles

x^{2} + y^{2} = r^{2}, r = 1, 2

and the rays given by

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

,

y > 0

is

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice I>Q 18

The maximum number of points with rational co-ordinates on a circle whose centre is

(\sqrt{3}, 0)

is: