Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 14

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

The set of values of $c,$ so that the equations $y = |x| + c$ and $x^{2} + y^{2} - 8 |x| - 9 = 0$ have no solution, is

50% studentsanswered this correctly

Important Questions on Circle

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 15

If

(1 + α x)^{n} = 1 + 8 x + 24 x^{2} + \dots

and a line through

P (α, n)

cuts the circle

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

in

A

and

B

, then

P A \cdot P B

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 16

A rhombus is inscribed in the region common to the two circles

x^{2} + y^{2} - 4 x - 12 = 0

and

x^{2} + y^{2} + 4 x - 12 = 0

with two of its vertices on the line joining the centres of the circles. The area of the rhombus is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 18

If the tangent at the point

P

on the circle

x^{2} + y^{2} + 6 x + 6 y = 2

meets the straight line

5 x - 2 y + 6 = 0

at a point

Q

on

Y

-axis, then the length of

P Q

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 19

The locus of the centre of a circle, which touches externally the circle

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

and also touches

Y

-axis, is given by the equation

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 20

If two circles with radii

a

and

b

touch each other externally such that

θ

is the angle between the direct common tangents

(a > b \geq 2)

, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 21

Equation of circumcircle of an equilateral

△ A B C

is

x^{2} + y^{2} + 2 a x + 2 b y = 0

. If one vertex of the triangle coincides with Origin then the equation of incircle of the

△ A B C

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 22

Equation of the circumcircle of equilateral

Δ A B C

is

x^{2} + y^{2} + 2 a x + 2 b y = 0 .

If one vertex of the triangle coincides with origin, then equation of incircle of

Δ A B C

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Target Exercises>Q 23

Let

P Q

and

R S

be tangents at the extremities of diameter

P R

of a circle of radius

r

. If

P S

and

R Q

intersect at a point

X

on the circumference of the circle, then

2 r

equals