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If one of the diagonal of a square is along the line $x = 2 y$ and one of its vertices is $(3, 0)$ , then its sides through this vertex are given by, the equations

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Important Questions on Straight Lines

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Let

L

be the line passing through the point

P (1, 2)

such that its intercepted segment between the co-ordinate axes is bisected at

P

. If

L_{1}

is the line perpendicular to

L

and passing through the point

(- 2, 1)

, then the point of intersection of

L

and

L_{1}

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Two sides of a parallelogram are along the lines,

x + y = 3

and

x - y + 3 = 0 .

If its diagonals intersect at

(2, 4),

then one of its vertex is:

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The point on the line

4 x - y - 2 = 0

which is equidistant from the points

(- 5, 6)

and

(3, 2)

is-

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

a, b

are positive real numbers such that the lines

a x + 9 y = 5 a n d 4 x + b y = 3

are parallel, then the least possible value of

a + b

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The number of values of $k$ , for which the system of equations :

$(k + 1) x + 8 y = 4 k$

$k x + (k + 3) y = 3 k - 1$

has no solution, is :

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

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 :

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

For $a > b > c > 0$ , the distance between $(1, 1)$ and the point of intersection of the lines $a x + b y + c = 0$ and $b x + a y + c = 0$ is less than $2 \sqrt{2}$ . Then

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A ray of light is incident along a line which meets another line

7 x - y + 1 = 0

at the point

(0, 1)

. The ray is then reflected from this point along the line

y + 2 x = 1

. Then the equation of the line of incidence of the ray of light is :

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Two vertices of a triangle are

(0, 2)

and

(4, 3) .

If its orthocenter is at the origin, then its third vertex lies in which quadrant?

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Distance between two parallel lines

y = 2 x + 4

and

y = 2 x - 1

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The line which is parallel to

x

-axis and crosses the curve

y = \sqrt{x}

at an angle

45 °

, is

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A ray of light along

x + \sqrt{3} y = \sqrt{3}

gets reflected upon reaching

X -

axis, the equation of the reflected ray is

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Given three points

P, Q, R

with

P (5, 3)

and

R

lies on the

x -

axis. If the equation of

R Q

x - 2 y = 2

and

P Q

is parallel to the

x -

axis, then the centroid of

Δ P Q R

lies on the line

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

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:

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

If a line

L

is perpendicular to the line

5 x - y = 1,

and the area of the triangle formed by the line

L

and the coordinate axes is

5

sq units, then the distance of the line

L

from the line

x + 5 y = 0

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Slope of a line passing through

P (2, 3)

and intersecting the line

x + y = 7

at a distance of

4

units from

P,

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The point

(2, 1)

is translated parallel to the line

L : x - y = 4

2 \sqrt{3}

units. If the new point

Q

lies in the third quadrant, then the equation of the line passing through

Q

and perpendicular to

L

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The equation of the line passing through

(a, b)

and parallel to the line

\frac{x}{a} + \frac{y}{b} = 1

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Let

a, b, c

and

d

be non-zero numbers. If the point of intersection of the lines

4 a x + 2 a y + c = 0 & 5 b x + 2 b y + d = 0

lies in the fourth quadrant and is equidistant from the two axes then

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The tangent to the curve

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

, parallel to the line

2 y = 4 x + 1

, also passes through the point :

If one of the diagonal of a square is along the line x=2y and one of its vertices is (3,0), then its sides through this vertex are given by, the equations

Important Questions on Straight Lines

Learn and Prepare for any exam you want !

If one of the diagonal of a square is along the line $x = 2 y$ and one of its vertices is $(3, 0)$ , then its sides through this vertex are given by, the equations