EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 25 June 2022 Shift 2>Q 82

MEDIUM

JEE Main

IMPORTANT

Earn 100

A circle touches both the $y$ -axis and the line $x + y = 0$ . Then the locus of its center is

46.15% studentsanswered this correctly

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 - 26 June 2022 Shift 1>Q 83

Let

R

be the point

(3, 7)

and let

P

and

Q

be two points on the line

x + y = 5

such that

P Q R

is an equilateral triangle. Then the area of

∆ P Q R

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 27 June 2022 Shift 1>Q 84

In an isosceles triangle

A B C

, the vertex

A

is

(6, 1)

and the equation of the base

B C

is

2 x + y = 4

. Let the point

B

lie on the line

x + 3 y = 7

. If

(α, β)

is the centroid

∆ A B C

, then

15 (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 - 27 June 2022 Shift 1>Q 85

A rectangle

R

with end points of the one of its sides as

(1, 2)

and

(3, 6)

is inscribed in a circle. If the equation of a diameter of the circle is

2 x - y + 4 = 0

, then the area of

R

is _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 27 June 2022 Shift 2>Q 86

Let a circle

C

of radius

5

lie below the

x

-axis. The line

L_{1} = 4 x + 3 y + 2

passes through the centre

P

of the circle

C

and intersects the line

L_{2} : 3 x - 4 y - 11 = 0

at

Q

. The line

L_{2}

touches

C

at the point

Q

. Then the distance of

P

from the line

5 x - 12 y + 51 = 0

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 28 June 2022 Shift 1>Q 87

A ray of light passing through the point

P (2, 3)

reflects on the

X

-axis at point

A

and the reflected ray passes through the point

Q (5, 4)

. Let

R

be the point that divides the line segment

A Q

internally into the ratio

2 : 1

. Let the co-ordinates of the foot of the perpendicular

M

from

R

on the bisector of the angle

P A Q

be

(α, β)

. Then, the value of

7 α + 3 β

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 28 June 2022 Shift 2>Q 88

Let a triangle be bounded by the lines

L_{1} : 2 x + 5 y = 10

;

L_{2} : - 4 x + 3 y = 12

and the line

L_{3}

, which passes through the point

P (2, 3)

, intersect

L_{2}

at

A

and

L_{1}

at

B

. If the point

P

divides the line-segment

A B

, internally in the ratio

1 : 3

, then the area of the triangle is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 28 June 2022 Shift 2>Q 89

If the system of linear equations

2 x - 3 y = γ + 5

α x + 5 y = β + 1

, where

α, β, γ \in R

has infinitely many solutions, then the value of

|9 α + 3 β + 5 γ|

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 29 June 2022 Shift 1>Q 90

The distance between the two points

A

and

A^{'}

which lie on

y = 2

such that both the line segments

A B

and

A^{'} B

(where

B

is the point

(2, 3)

) subtend angle

\frac{π}{4}

at the origin, is equal to