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JEE Main

IMPORTANT

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Let $P$ be a variable point on the parabola $y = 4 x^{2} + 1 .$ Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y = x$ is:

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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 - 20 July 2021 Shift 2>Q 9

Consider a triangle having vertices

A (- 2, 3), B (1, 9)

and

C (3, 8) .

If a line

L

passing through the circum-centre of triangle

A B C,

bisects line

B C,

and intersects

y

-axis at point

(0, \frac{α}{2}),

then the value of real number

α

is _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 25 July 2021 Shift 2>Q 10

Let the equation of the pair of lines,

y = p x

and

y = q x,

can be written as

(y - p x) (y - q x) = 0 .

Then the equation of the pair of the angle bisectors of the lines

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

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 27 July 2021 Shift 2>Q 11

Two sides of a parallelogram are along the lines

4 x + 5 y = 0

and

7 x + 2 y = 0 .

If the equation of one of the diagonals of the parallelogram is

11 x + 7 y = 9,

then other diagonal passes through the point:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main 16 March 2021 Shift 2>Q 12

Let

A (- 1, 1), B (3, 4)

and

C (2, 0)

be given three points. A line

y = m x, m > 0

, intersects lines

A C

and

B C

at point

P

and

Q

respectively. Let

A_{1}

and

A_{2}

be the areas of

Δ A B C

and

Δ P Q C

respectively, such that

A_{1} = 3 A_{2}

, then the value of

m

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main 17 March 2021 Shift 1>Q 13

In a triangle

P Q R,

the co-ordinates of the points

P

and

Q

are

(- 2, 4)

and

(4, - 2)

respectively. If the equation of the perpendicular bisector of

P R

2 x - y + 2 = 0,

then the centre of the circumcircle of the

Δ P Q R

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main 17 March 2021 Shift 2>Q 14

Let

\tan α, \tan β

and

\tan γ; α, β, γ \neq \frac{(2 n - 1) π}{2}, n \in N

be the slopes of the three line segments

O A, O B

and

O C,

respectively, where

O

is origin. If circumcentre of

Δ A B C

coincides with origin and its orthocentre lies on

y

-axis, then the value of

{(\frac{\cos 3 α + \cos 3 β + \cos 3 γ}{\cos α \cdot \cos β \cdot \cos γ})}^{2}

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main 18 March 2021 Shift 1>Q 15

The number of integral values of

m

so that the abscissa of point of intersection of lines

3 x + 4 y = 9

and

y = m x + 1

is also an integer, is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main 18 March 2021 Shift 1>Q 16

The equation of one of the straight lines which passes through the point

(1, 3)

and makes an angles

\tan^{- 1} (\sqrt{2})

with the straight line,

y + 1 = 3 \sqrt{2} x

Let P be a variable point on the parabola y=4x2+1. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y=x is:

Important Questions on Point and Straight Line

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Let $P$ be a variable point on the parabola $y = 4 x^{2} + 1 .$ Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y = x$ is: