Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 46

HARD

JEE Advanced

IMPORTANT

Earn 100

Circles are drawn through the point $(2, 0)$ to cut intercept of length $5$ units on $x$ -axis. If centre of one such circle lies in the first quadrant, then the equation of this circle 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>Entrances Gallery>Q 47

Two vertices of an equilateral triangle are

(- 1, 0)

and

(1, 0)

. The equation of its circumcircle is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 48

The least and greatest distances of the point

(10, 7)

from the circle

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

are

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 49

Equation of unit circle concentric with circle

x^{2} + y^{2} + 8 x + 4 y - 8 = 0

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 50

If

a > 2 b > 0

, then the positive value of

m

, for which

y = m x - b \sqrt{1 + m^{2}}

is a common tangent to

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

and

{(x - a)}^{2} + y^{2} = b^{2}

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 51

The equation of the two tangents from

(- 5, - 4)

to the circle

x^{2} + y^{2} + 4 x + 6 y + 8 = 0

are

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 52

The locus of mid-points of chord of the circle

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

which subtends a right angle at the origin is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 53

The circle

x^{2} + y^{2} - 6 x - 8 y = 0

and

x^{2} + y^{2} - 6 x + 8 = 0

are

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 13 - Circle>Entrances Gallery>Q 54

If the circle

x^{2} + y^{2} + 2 x + 2 k y + 6 = 0

and

x^{2} + y^{2} + 2 k y + k = 0

intersect orthogonally, then

k

is equal to