EASY

Earn 100

Which among the following represents the combined equation of a pair of lines through point $(1, 0)$ and parallel to the lines represented by $2 x^{2} - x y - y^{2} = 0$ .

50% studentsanswered this correctly

Important Questions on Pair of Straight lines

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The product of the length of perpendiculars from origin to the pair of lines

x^{2} + 3 y^{2} + 4 x y - 4 x - 10 y + 3 = 0

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The normal to the curve

x^{2} + 2 x y - 3 y^{2} = 0

, at

(1, 1)

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The angle by which axes are to be rotated without changing the origin so that the transformed equation of

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

in new coordinates

(X, Y)

does not contain

X Y

term is

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The line

5 x + y - 1 = 0

coincides with one of the lines given by

5 x^{2} + x y - k x - 2 y + 2 = 0

then the value of

k

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

' m_{1}'

and

' m_{2}'

(m_{1} > m_{2})

are the slopes of the lines represented by

5 x^{2} - 8 x y + 3 y^{2} = 0

, then

m_{1} : m_{2}

equals

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The point of intersection of lines represented by

x^{2} - y^{2} + x + 3 y - 2 = 0

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

If the acute angle between lines

a x^{2} + 2 h x y + b y^{2} = 0

\frac{π}{4}

, then

4 h^{2} =

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

x^{2} + y^{2} + 2 g x + 2 f y + 1 = 0

represents a pair of straight lines, then

f^{2} + g^{2}

is equal to

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The equation of the pair of straight lines perpendicular to the pair

2 x^{2} + 3 x y + 2 y^{2} + 10 x +

5 y = 0

and passing though the origin is______

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

9 x^{2} - 24 x y + 16 y^{2} + α x + β y + 6 = 0

represents a pair of parallel lines of

1

unit apart and one of those lines passes through

(1, 1)

then

\frac{α}{β} =

MEDIUM

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

If slopes of lines represented by

K x^{2} + 5 x y + y^{2} = 0

differ by

1

then

K =

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The equation

4 x^{2} - 24 x y + 11 y^{2} = 0

represents

MEDIUM

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

If lines represented by equation

p x^{2} - q y^{2} = 0

are distinct then

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

Consider the lines

L_{1} \equiv 4 x + 5 y - 6 = 0, L_{2} \equiv 2 x + 3 y - 4 = 0, L_{3} \equiv 3 x - y + 2 = 0 .

If the line

L_{1} = 0

intersects the lines

L_{2} = 0

and

L_{3} = 0

at the points

A

and

B

respectively, then the combined equation of

O A

and

O B

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

θ

is the angle between the pair of straight lines

x^{2} - 5 x y + 4 y^{2} + 3 x - 4 = 0

,

then

\tan^{2} θ

is equal to

HARD

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

(a + 3 b) (3 a + b) = 4 h^{2}

, then the angle between the lines represented by

a x^{2} + 2 h x y + b y^{2} = 0

HARD

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

If the slope of one of the lines represented by

a x^{2} + 2 h x y + b y^{2} = 0

be the square of the other, then

\frac{a + b}{h} + \frac{8 h^{2}}{a b}

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

Find the angle between the pair of lines represented by the equation

x^{2} + 4 x y + y^{2} = 0

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The angle between the pair of straight lines

3 y^{2} - 8 x y - 3 x^{2} - 29 x + 3 y - 18 = 0

EASY

Mathematics>Coordinate Geometry>Pair of Straight lines>Equations of Pair of Lines

The value of '

p

' for which the equation

x^{2} + p x y + y^{2} - 5 x - 7 y + 6 = 0

represents a pair of straight lines, is

Which among the following represents the combined equation of a pair of lines through point (1,0) and parallel to the lines represented by 2x2-xy-y2=0.

Important Questions on Pair of Straight lines

Learn and Prepare for any exam you want !

Which among the following represents the combined equation of a pair of lines through point $(1, 0)$ and parallel to the lines represented by $2 x^{2} - x y - y^{2} = 0$ .