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The slopes of the lines represented by $x^{2} + 2 h x y + 2 y^{2} = 0$ are in the ratio $1 : 2,$ then $h$ equals

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Important Questions on Straight Line and Pair of Straight Lines

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Entrances Gallery>Q 28

Let

A (2, - 3)

and

B (- 2, 1)

be vertices of a

Δ A B C

. If the centroid of this triangle moves on the line

2 x + 3 y = 1

then the locus of the vertex

C

is the line

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Entrances Gallery>Q 29

A straight line passes through the points

(5, 0)

and

(0, 3)

. The length of perpendicular from the point

(4, 4)

on the line is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Entrances Gallery>Q 30

p

is the length of the perpendicular from the origin to the line, whose intercepts on the coordinate axes are

\frac{1}{3}

and

\frac{1}{4},

then the value of

p

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Entrances Gallery>Q 31

p

and

q

are respectively the perpendiculars from the origin upon the straight lines, whose equations are

x \sec θ + y cosec θ = a

and

x \cos θ - y \sin θ = a \cos 2 θ

, then

4 p^{2} + q^{2}

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>Entrances Gallery>Q 32

If any point

P

is at the equal distances from points

A (a + b, a - b)

and

B (a - b, a + b)

, then locus of point

P

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Entrances Gallery>Q 33

The equation of the perpendicular bisector of the line segment joining

A (- 2, 3)

and

B (6, - 5)

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Entrances Gallery>Q 34

The equation of second degree

x^{2} + 2 \sqrt{2} x y + 2 y^{2} + 4 x + 4 \sqrt{2} y + 1 = 0

represents a pair of straight lines. The distance between them is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 12 - Straight Line and Pair of Straight Lines>Entrances Gallery>Q 35

Let

P = (- 1, 0), O = (0, 0)

and

Q = (3, 3 \sqrt{3})

be three points. Then, the equation of the bisector of the

∠ P O Q

The slopes of the lines represented by x2+2hxy+2y2=0 are in the ratio 1:2, then h equals

Important Questions on Straight Line and Pair of Straight Lines

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The slopes of the lines represented by $x^{2} + 2 h x y + 2 y^{2} = 0$ are in the ratio $1 : 2,$ then $h$ equals