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

HARD

JEE Main

IMPORTANT

Earn 100

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

50% studentsanswered this correctly

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 11

Consider the circle

x^{2} + y^{2} - 8 x - 18 y + 93 = 0

with center

C

and point

P (2, 5)

outside it. From the point

P

, tangents

P Q

and

P R

are drawn to the circle with

S

as the midpoint of

Q R

. The line joining

P

to

C

intersects the given circle at

A

and

B

. Which of the following hold(s) good?

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 12

Consider two circles

C_{1} : x^{2} + y^{2} - 1 = 0

and

C_{2} : x^{2} + y^{2} - 2 = 0

. Let

A (1, 0)

be a fixed point on the circle

C_{1}

and

B

be any variable point on the circle

C_{2}

. The line

B A

meets the curve

C_{2}

again at

C

. Which of the following is/are correct?

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 1

If

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

is tangent to a circle for all

m \in [- 1, 1]

, then the radius of the circle is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 4 - Circles>DPP>Q 2

If the line

3 x - 4 y - λ = 0

touches the circle

x^{2} + y^{2} - 4 x - 8 y - 5 = 0

at

(a, b)

, then which of the following is not the possible value of

λ + a + b

?

MEDIUM

JEE Main

IMPORTANT

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

The normal at the point

(3, 4)

on a circle cuts the circle at the point

(- 1, - 2)

. Then the equation of the circle is

EASY

JEE Main

IMPORTANT

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

For all values of

m \in R

, the line

y - m x + m - 1 = 0

cuts the circle

x^{2} + y^{2} - 2 x - 2 y + 1 = 0

at an angle

HARD

JEE Main

IMPORTANT

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

If the line

|y| = x - α, α > 0

does not meet the circle

x^{2} + y^{2} - 10 x + 21 = 0

, then

α \in

MEDIUM

JEE Main

IMPORTANT

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

Let

C

be the circle of unit radius centred at the origin. If two positive numbers

x_{1}

and

x_{2}

are such that the line passing through

(x_{1}, - 1)

and

(x_{2}, 1)

is tangent to

C

, then