HARD

JEE Main

IMPORTANT

Earn 100

A line, with the slope greater than one, passes through the point $A (4, 3)$ and intersects the line $x - y - 2 = 0$ at the point $B$ . If the length of the line segment $A B$ is $\frac{\sqrt{29}}{3}$ , then $B$ also lies on the line

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Important Questions on Point and Straight Line

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 25 July 2022 Shift 2>Q 93

Let the point

P (α, β)

be at a unit distance from each of the two lines

L_{1} : 3 x - 4 y + 12 = 0

, and

L_{2} : 8 x + 6 y + 11 = 0

. If

P

lies below

L_{1}

and above

L_{2}

, then

100 (α + β)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 26 July 2022 Shift 1>Q 94

A point

P

moves so that the sum of squares of its distances from the points

(1, 2)

and

(- 2, 1)

14

. Let

f (x, y) = 0

be the locus of

P

, which intersects the

x

-axis at the points

A, B

and the

y

-axis at the point

C, D

. Then the area of the quadrilateral

A C B D

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 26 July 2022 Shift 1>Q 95

The equations of the sides

A B, B C

and

C A

of a triangle

A B C

are

2 x + y = 0, x + p y = 15 a

and

x - y = 3

respectively. If its orthocentre is

(2, a)

- \frac{1}{2} < a < 2

, then

p

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 27 July 2022 Shift 1>Q 96

Let $A (1, 1), B (- 4, 3), C (- 2, - 5)$ be vertices of a triangle $A B C, P$ be a point on side $B C$ , and $Δ_{1}$ and $Δ_{2}$ be the areas of triangle $A P B$ and $A B C$ .

Respectively.

If $Δ_{1} : Δ_{2} = 4 : 7$ , then the area enclosed by the lines $A P, A C$ and the $x$ -axis is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 27 July 2022 Shift 2>Q 97

The equations of the sides

A B, B C

and

C A

of a triangle

A B C

are

2 x + y = 0, x + p y = 39

and

x - y = 3

respectively and

P (2, 3)

is its circumcentre. Then which of the following is NOT true

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 29 July 2022 Shift 1>Q 98

Let the circumcentre of a triangle with vertices

A (a, 3), B (b, 5)

and

C (a, b), a b > 0

P (1, 1)

. If the line

A P

intersects the line

B C

at the point

Q (k_{1}, k_{2})

, then

k_{1} + k_{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 29 July 2022 Shift 2>Q 99

Let

m_{1}, m_{2}

be the slopes of two adjacent sides of a square of side

a

such that

a^{2} + 11 a + 3 (m_{1}^{2} + m_{2}^{2}) = 220

. If one vertex of the square is

(10 (\cos α - \sin α), 10 (\sin α + \cos α))

, where

α \in (0, \frac{π}{2})

and the equation of one diagonal is

(cosα - sinα) x + (\sin α + \cos α) y = 10

, then

72 (\sin^{4} α + \cos^{4} α) + a^{2} - 3 a + 13

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 29 July 2022 Shift 2>Q 100

Let

A (α, - 2), B (α, 6)

and

C (\frac{α}{4}, - 2)

be vertices of a

∆ A B C

. If

(5, \frac{α}{4})

is the circumcentre of

∆ A B C

, then which of the following is NOT correct about

∆ A B C

A line, with the slope greater than one, passes through the point A4,3 and intersects the line x-y-2=0 at the point B. If the length of the line segment AB is 293, then B also lies on the line

Important Questions on Point and Straight Line

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A line, with the slope greater than one, passes through the point $A (4, 3)$ and intersects the line $x - y - 2 = 0$ at the point $B$ . If the length of the line segment $A B$ is $\frac{\sqrt{29}}{3}$ , then $B$ also lies on the line