The circle C 1 : x 2 + y 2 = 3 , with centre at O, intersects the parabola x 2 = 2 y at the point P in the first quadrant. Let the tangent to the circle C 1 at P touches other two circles C 2 and C 3 at R 2 and R 3 , respectively. Suppose C 2 and C 3 have equal radii 2 3 and centres Q 2 and Q 3 , respectively. If Q 2 and Q 3 lie on the y - axis, then

area of the triangle O R 2 R 3 is 6 2

area of the triangle P Q 2 Q 3 is 4 2

HARD

JEE Advanced

IMPORTANT

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A circle S passes through the point $(0, 1)$ and is orthogonal to the circles ${(x - 1)}^{2} + y^{2} = 16$ and $x^{2} + y^{2} = 1$ . Then

100% studentsanswered this correctly

Important Questions on Circle

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 2 - 2018>Q 3

Let

T

be the line passing through the points

P (- 2, 7)

and

Q (2, - 5)

. Let

F_{1}

be the set of all pairs of circles

(S_{1}, S_{2})

such that

T

is tangents to

S_{1}

P

and tangent to

S_{2}

Q

, and also such that

S_{1}

and

S_{2}

touch each other at a point, say,

M

. Let

E_{1}

be the set representing the locus of

M

as the pair

(S_{1}, S_{2})

varies in

F_{1}

. Let the set of all straight line segments joining a pair of distinct points of

E_{1}

and passing through the point

R (1,1)

F_{2}

. Let

E_{2}

be the set of the mid-points of the line segments in the set

F_{2}

. Then, which of the following statement(s) is (are) TRUE?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 2 - 2015>Q 4

Let

E_{1}

and

E_{2}

be two ellipse whose centers are at the origin. The major axes of

E_{1} & E_{2}

lie along the

x

-axis and the

y

-axis, respectively. Let

S

be the circle

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

The straight line

x + y = 3

touches the curves

S, E_{1}

and

E_{2}

P, Q

and

R,

respectively. Suppose that

P Q = P R = \frac{2 \sqrt{2}}{3}

. If

e_{1}

and

e_{2}

are the eccentricities of

E_{1}

and

E_{2},

respectively, then the correct expression(s) is(are)

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 2 - 2013>Q 5

Equation of circle(s) touching

x

-axis at a distance

3

from the origin and having an intercept of length

2 \sqrt{7}

y

-axis is (are)

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 1 - 2021>Q 6

Consider a triangle

Δ

whose two sides lie on the

x

-axis and the line

x + y + 1 = 0

. If the orthocenter of

Δ

(1, 1)

, then the equation of the circle passing through the vertices of the triangle

Δ

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 1 - 2019>Q 7

A line

y = m x + 1

intersects the circle

{(x - 3)}^{2} + {(y + 2)}^{2} = 25

at the points

P

and

Q .

If the midpoint of the line segment

P Q

has

x -

coordinate

- \frac{3}{5},

then which one of the following options is correct?

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 1 - 2019>Q 8

Let the point

B

be the reflection of the point

A (2, 3)

with respect to the line

8 x - 6 y - 23 = 0 .

Let

T_{A}

and

T_{B}

be circle of radii

2

and

1

with centres

A

and

B

respectively. Let

T

be a common tangent to the circle

T_{A}

and

T_{B}

such that both the circle are on the same side of

T .

C

is the point of intersection of

T

and the line passing through

A

and

B,

then the length of the line segment

A C

is ___________.

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 1 - 2017>Q 11

Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.

Column 1	Column 2	Column 3
(I) $x^{2} + y^{2} = a^{2}$	(i) $m y = m^{2} x + a$	(P) $(\frac{a}{m^{2}}, \frac{2 a}{m})$
(II) $x^{2} + a^{2} y^{2} = a^{2}$	(ii) $y = m x + a \sqrt{m^{2} + 1}$	(Q) $(\frac{- m a}{\sqrt{m^{2} + 1}}, \frac{a}{\sqrt{m^{2} + 1}})$
(III) $y^{2} = 4 a x$	(iii) $y = m x + \sqrt{a^{2} m^{2} - 1}$	(R) $(\frac{- a^{2} m}{\sqrt{a^{2} m^{2} + 1}}, \frac{1}{\sqrt{a^{2} m^{2} + 1}})$
(IV) $x^{2} - a^{2} y^{2} = a^{2}$	(iv) $y = m x + \sqrt{a^{2} m^{2} + 1}$	(S) $(\frac{- a^{2} m}{\sqrt{a^{2} m^{2} - 1}}, \frac{- 1}{\sqrt{a^{2} m^{2} - 1}})$

For

a = \sqrt{2}

, if a tangent is drawn to a suitable conic (Column 1) at the point of contact

(- 1, 1)

, then which of the following options is the only Correct combination for obtaining its equation?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Circle>JEE Advanced Paper 1 - 2016>Q 12

Let

R S

be the diameter of the circle

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

where,

S

is the point

(1, 0)

. Let

P

be a variable point (other than

R & S

) on the circle and tangents to the circle at

S & P

meet at the point

Q

. The normal to the circle at

P

intersects a line drawn through

Q

parallel to

R S

at point

E

. Then, the locus of

E

passes through the point (s):

A circle S passes through the point (0, 1) and is orthogonal to the circles x-12+y2=16 and x2+y2=1. Then

Important Questions on Circle

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A circle S passes through the point $(0, 1)$ and is orthogonal to the circles ${(x - 1)}^{2} + y^{2} = 16$ and $x^{2} + y^{2} = 1$ . Then