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The equation of the locus of the foot of perpendicular drawn from $(5,6)$ on the family of lines $(x - 2) + λ (y - 3) = 0$ (where $λ \in R$ ) is

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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 :

The equation of the locus of the foot of perpendicular drawn from 5,6 on the family of lines x-2+λy-3=0 (where λ∈R) is

Important Questions on Straight Lines

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The equation of the locus of the foot of perpendicular drawn from $(5,6)$ on the family of lines $(x - 2) + λ (y - 3) = 0$ (where $λ \in R$ ) is