MEDIUM

JEE Main

IMPORTANT

Earn 100

Let the circumcentre of a triangle with vertices $A (a, 3), B (b, 5)$ and $C (a, b), a b > 0$ be $P (1, 1)$ . 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

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Important Questions on Point and Straight Line

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

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 24 January 2023 Shift 2>Q 101

The equations of the sides

A B, B C & C A

of a triangle

A B C

are

2 x + y = 0

x + p y = 21 a

(a \neq 0)

and

x - y = 3

respectively. Let

P (2, a)

be the centroid of the triangle

A B C

, then

{(B C)}^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 25 January 2023 Shift 2>Q 102

A triangle is formed by

X

-axis,

Y

-axis and the line

3 x + 4 y = 60

. Then the number of points

P (a, b)

which lie strictly inside the triangle, where

a

is an integer and

b

is a multiple of

a

, is _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 29 January 2023 Shift 1>Q 103

A light ray emits from the origin making an angle

30 °

with the positive

x -

axis. After getting reflected by the line

x + y = 1

, if this ray intersects

x -

axis at

Q

, then the abscissa of

Q

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 29 January 2023 Shift 1>Q 104

Let

B

and

C

be the two points on the line

y + x =0

such that

B

and

C

are symmetric with respect to the origin. Suppose

A

is a point on

y - 2 x = 2

such that

∆ A B C

is an equilateral triangle. Then, the area of the

∆ A B C

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 30 January 2023 Shift 1>Q 105

A straight line cuts off the intercepts $\mathrm{OA}=\mathrm{a}$ and $\mathrm{OB}=\mathrm{b}$ on the positive directions of $\mathrm{x}$-axis and $\mathrm{y}-$ axis respectively. If the perpendicular from origin $\mathrm{O}$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the area of $\triangle \mathrm{OAB}$ is $\frac{98}{3} \sqrt{3}$, then $\mathrm{a}^2-\mathrm{b}^2$ is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 1 February 2023 Shift 1>Q 106

If the orthocentre of the triangle, whose vertices are

(1, 2), (2, 3)

and

(3, 1)

(α, β)

, then the quadratic equation whose roots are

α + 4 β

and

4 α + β

, is

Let the circumcentre of a triangle with vertices Aa,3,Bb,5 and Ca,b,ab>0 be P1,1. If the line AP intersects the line BC at the point Qk1,k2, then k1+k2 is equal to

Important Questions on Point and Straight Line

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Let the circumcentre of a triangle with vertices $A (a, 3), B (b, 5)$ and $C (a, b), a b > 0$ be $P (1, 1)$ . 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