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The portion of the line $4 x + 5 y = 20$ in the first quadrant is trisected by the lines $L_{1}$ and $L_{2}$ passing through the origin. The tangent of an angle between the lines $L_{1}$ and $L_{2}$ is :

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Important Questions on The Straight Line

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

The angle between lines

\sqrt{3 x} + y = 1

and

x + \sqrt{3 y} = 1

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

The acute angle included between the lines

x \sin θ - y \cos θ = 5

and

x \sin α - y \cos α + 11 = 0

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

The tangent of the angle between the lines whose intercepts on the axes are respectively

a, - b

and

b, - a

, is

EASY

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

Let

A B C

be a triangle with

A (- 3, 1)

and

∠ A C B = θ, 0 < θ < \frac{π}{2}

. If the equation of the median through

B

2 x + y - 3 = 0

and the equation of angle bisector of

C

7 x - 4 y - 1 = 0

, then

\tan θ

is equal to:

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

The locus of the mid-points of the perpendiculars drawn from points on the line

x = 2 y

, to the line

x = y

, is.

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

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

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

A straight line through the point

(3, - 2)

is inclined at an angle

60 °

to the line

\sqrt{3} x + y = 1

. If it intersects the

X -

axis, then its equation will be

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

In a

∆ A B C, 2 x + 3 y + 1 = 0, x + 2 y - 12 = 0

are the perpendicular bisectors of its sides

A B

and

A C

respectively and if

A

(3, 2),

then the slope of the side

B C

EASY

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

Answer the question on the basis of the following figure.

If AB is parallel to EC and $∠ B C D = 72^{°}$ , what will be that value of $∠ B A C$ ?

Question Image

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

A triangle

A B C

lying in the first quadrant has two vertices as

A (1, 2)

and

B (3, 1)

. If

∠ B A C = 90^{o},

and

ar (Δ ABC) = 5 \sqrt{5}

sq. units, then the abscissa of the vertex

C

is :

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

If the two lines

\frac{3}{2} x + (2 a - 1) y = 3

and

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

are perpendicular, then the distance of their point of intersection from the point

(1, 1)

HARD

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

A straight line

L

through the point

(3, - 2)

is inclined at an angle of

60 °

to the line

\sqrt{3} x + y = 1 .

L

also intersects the

X

-axis, then the equation of

L

is:

EASY

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

If the tangent at a point

P

on the curve

y = 4 x^{4} + x

is perpendicular to the tangent to the same curve at

(0, 0),

then the point

P

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

The medians

A D

and

B E

of a triangle with vertices

A (0, b), B (0, 0)

and

C (a, 0)

are perpendicular to each other, if

EASY

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

In an isosceles right angled triangle, if the equation of the hypotenuse and its opposite vertex are

3 x + 4 y = 4

and

(2, 2),

then the slopes of the remaining two sides are

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

If the equation of a line having a slope

m (m \in Z),

passing through

(1, 1)

and making an angle of

\tan^{- 1} (\frac{5}{7})

with the line

x + y - 3 = 0

a x + y + c = 0,

then

a c =

EASY

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

The slope of a line

L

2 .

m_{1}, m_{2}

are slopes of two lines which are inclined at an angle of

\frac{π}{6}

with

L,

then

m_{1} + m_{2} =

HARD

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

Straight lines

3 x + 4 y = 5

and

4 x - 3 y = 15

intersect at the point

A

. If point

B

and

C

are chosen on these two lines such that

A B = A C

, then the possible equation of the line

B C

passing through the point

(1, 2)

HARD

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

The line which is parallel to

x

-axis and crosses the curve

y = \sqrt{x}

at an angle

45 °

, is

HARD

Mathematics>Coordinate Geometry>The Straight Line>Intersection of Straight Lines

If the straight line

2 x - 3 y + 17 = 0

is perpendicular to the line passing through the points

(7, 17)

and

(15, β)

, then

β

equals :

The portion of the line 4x+5y=20 in the first quadrant is trisected by the lines L1 and L2 passing through the origin. The tangent of an angle between the lines L1 and L2 is :

Important Questions on The Straight Line

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The portion of the line $4 x + 5 y = 20$ in the first quadrant is trisected by the lines $L_{1}$ and $L_{2}$ passing through the origin. The tangent of an angle between the lines $L_{1}$ and $L_{2}$ is :