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JEE Advanced

IMPORTANT

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The centroid of an equilateral triangle is $(0, 0)$ . If two vertices of the triangle lie on $x + y = 2 \sqrt{2},$ then one of them will have its coordinates as

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Important Questions on Straight Line and Pair of Straight Lines

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 47

A B C

is an equilateral triangle such that the vertices

B

and

C

lie on two parallel lines at a distance

6 .

A

lies between the parallel lines at a distance

4

from one of them, then the length of a side of the equilateral triangle is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 48

If the straight lines

a_{1} x + b_{1} y + c_{1} = 0

a_{1} x + b_{1} y + c_{2} = 0, a_{2} x + b_{2} y + d_{1} = 0

and

a_{2} x + b_{2} y + d_{2} = 0

are the sides of rhombus, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 49

A straight line

L_{1}

makes angle

\tan^{- 1} \frac{4}{3}

with the parallel lines

3 x - 4 y - 24 = 0

and

3 x - 4 y - 12 = 0

L_{1}

makes an intercept of

3

units with these parallel lines, then the equation

L_{1}

may be given as

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 50

The vertices of a

Δ O B C

are

O (0, 0), B (- 3, - 1)

and

C (- 1, - 3)

. The equation of a line parallel to

B C

and intersecting sides

O B

and

O C

whose distance from the origin is

\frac{1}{2},

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 51

The image of the point

P (3, 5)

with respect to the line

y = x

is the point

Q, R

is the image of

Q

with respect to the line

y = 0

is the point

R (a, b),

then

(a, b)

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 52

The equation of the diagonal through origin of the quadrilateral formed by the line

x = 0, y = 0, x + y - 1 = 0

and

6 x + y - 3 = 0

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 53

Consider a family of straight lines

(x + y) + λ (2 x - y + 1) = 0

. Equation of the straight line belonging to this family that is farthest from

(1, - 3)

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Target Exercises>Q 54

A family of lines is given by

(1 + 2 λ) x + (1 - λ) y + λ = 0, λ

being the parameter. The line belonging to this family at the maximum distance from the point

(1, 4)

The centroid of an equilateral triangle is (0,0) . If two vertices of the triangle lie on x+y=22, then one of them will have its coordinates as

Important Questions on Straight Line and Pair of Straight Lines

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The centroid of an equilateral triangle is $(0, 0)$ . If two vertices of the triangle lie on $x + y = 2 \sqrt{2},$ then one of them will have its coordinates as