MEDIUM

JEE Main

IMPORTANT

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If the curves $\frac{x^{2}}{4} + y^{2} = 1$ and $\frac{x^{2}}{a^{2}} + y^{2} = 1$ for a suitable value of $a$ , cut on four concyclic points, the equation of circle passing through these four points, is

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Important Questions on Circles

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 3

A B

is a chord of

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

and

P (1, 1)

trisects

A B .

Then the length of the chord

A B

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 4

$A B$ is a chord of the circle $x^{2} + y^{2} = \frac{25}{2}$ . $P$ is a point such that $P A = 4, P B = 3 .$ If $A B = 5,$ then distance of $P$ from the origin can be

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 5

Chord

AB

of the circle

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

passes through the point

(7, 1)

and subtends an angle of

60 °

at the circumference of the circle. If

m_{1}

and

m_{2}

are the slopes of two such chords, then the value of

m_{1} m_{2}

is.

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 6

P

and

Q

are the two points on a line passing through

(2, 4)

and having slope

m

. If a line segment

A B

subtends a right angle at

P

and

Q,

where

A = (0, 0)

and

B = (6, 0),

then range of values of

m

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 7

In the

xy -

plane, the length of the shortest path from

(0, 0)

(12, 16)

that does not go inside the circle

{(x - 6)}^{2} + {(y - 8)}^{2} = 25 .

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 8

Triangle

ABC

is right-angled at

A

. The circle with center

A

and radius

AB

cuts

BC

and

AC

internally at

D

and

E

, respectively. If

BD = 20

and

DC = 16

then the length

AC

equals

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 9

All chords through an external point to the circle

x^{2} + y^{2} = 16

are drawn having length

l

which is a positive integer. The sum of the squares of the distances from the center of the circle to these chords is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 10

The line

3 x + 6 y = k

intersects the curve

2 x^{2} + 2 x y + 3 y^{2} = 1

at points

A

and

B

. The circle on

AB

as diameter passes through the origin. The possible value/values of $k$ is/are

If the curves x24+y2=1 and x2a2+y2=1 for a suitable value of a, cut on four concyclic points, the equation of circle passing through these four points, is

Important Questions on Circles

Learn and Prepare for any exam you want !

If the curves $\frac{x^{2}}{4} + y^{2} = 1$ and $\frac{x^{2}}{a^{2}} + y^{2} = 1$ for a suitable value of $a$ , cut on four concyclic points, the equation of circle passing through these four points, is