The region represented by the inequation system x ≥ 0 , y ≥ 0 , x ≤ y , x + 3 y ≤ 60 , x + y ≥ 10 is

unbounded in the first quadrant

unbounded in the second quadrant

HARD

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Consider two lines $L_{1}$ and $L_{2}$ given by $3 x + 4 y - 7 = 0$ and $4 x - 3 y - 1 = 0$ respectively and a variable point $P$ . Let $d (P, L_{i}), i = 1, 2$ represents the perpendicular distance of point $P$ from the line $L_{i}$ . If point $P$ moves in a certain region $R$ in such a way that $6 \leq 2 d (P, L_{1}) + 3 d (P, L_{2}) \leq 12$ , then the area of the region $R$ :

Important Questions on Straight Line

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

Let

a \neq 0, b \neq 0, c

be three real numbers and

L (p, q) = \frac{a p + b q + c}{\sqrt{a^{2} + b^{2}}}, \forall p, q \in R

. If

L (\frac{2}{3}, \frac{1}{3}) + L (\frac{1}{3}, \frac{2}{3}) + L (2, 2) = 0

, then the line

a x + b y + c = 0

always passes through the fixed point

HARD

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

A ray of light is projected from the origin at angle of

60 °

with the positive direction of

x

-axis towards the line,

y = 2,

which gets reflected from the point,

(α, 2) .

Then the distance of the reflected ray of light from the point

(2, 2)

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

If the family of straight lines

a x + b y + c = 0

, where

2 a + 3 b = 4 c

is concurrent at the point

P (l, m)

, then the foot of the perpendicular drawn from

P

to the line

x + y + 1 = 0

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The line passing through the points

(1, 2, - 1)

and

(3, - 1, 2)

meets the

y z

-plane at which one of the following points?

EASY

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The coordinates of the foot of the perpendicular from the point

(2, 3)

on the line

x + y - 11 = 0

EASY

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The foot of the perpendicular drawn from the point

(1, 8, 4)

on the line joining the point

(0, - 11, 4)

and

(2, - 3, 1)

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The length of the perpendicular from

(1, - 2)

to the line

12 x + 5 y + 63 = 0

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The image of the point

(3, 5)

in the line

x - y + 1 = 0

, lies on :

EASY

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The reflection of the point

(α, β, γ)

in the

x y -

plane is

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The set of all possible values of

θ

in the interval

(0, π)

for which the points

(1, 2)

and

(\sin θ, \cos θ)

lie on the same side of the line

x + y = 1

is?

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

Let

S

be a subset of the plane defined by

S = \{(x, y) : | x | + 2 | y | = 1\}

. Then, the radius of the smallest circle with centre at the origin and having non-empty intersection with

S

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

A point on the straight line,

3 x + 5 y = 15

which is equidistant from the coordinate axes will lie only in:

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

If the point

(a, a)

falls between the lines

|x + y| = 4,

then

EASY

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The polar coordinate of a point

P

(2, - \frac{π}{4}) .

The polar coordinate of the point

Q

which is such that line joining

P Q

is bisected perpendicularly by the initial line, is

HARD

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

A

ray of light passing through the point

(1, 2)

is reflected on the

x

-axis at a point

P

and passes through the point

(5, 3)

then the abscissa of a point

P

EASY

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

The region represented by the inequation system

x \geq 0, y \geq 0, x \leq y, x + 3 y \leq 60, x + y \geq 10

HARD

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

C

is the reflection of

A (2, 4)

x

-axis and

B

is the reflection of

C

y

-axis then

|A B|

is -

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

A ray of light coming from the point $(2, 2 \sqrt{3})$ is incident at an angle $30 °$ on the line $x = 1$ at the point $A$ . The ray gets reflected on the line $x = 1$ and meets $x$ -axis at the point $B$ . Then, the line $A B$ passes through the point

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

If $Q (0, - 1, - 3)$ is the image of the point $P$ in the plane $3 x - y + 4 z = 2$ and $R$ is the point $(3, - 1, - 2)$ , then the area (in sq. units) of $Δ P Q R$ is

Question Image

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Distance of a Point From a Line

If the points

(1, 1, λ) & (- 3, 0, 1)

, are equidistant from the plane,

3 x + 4 y - 12 z + 13 = 0,

then

λ

satisfies the equation:

Consider two lines L1 and L2 given by 3x+4y-7=0 and 4x-3y-1=0 respectively and a variable point P. Let dP,Li, i=1,2 represents the perpendicular distance of point P from the line Li. If point P moves in a certain region R in such a way that 6≤2dP,L1+3dP,L2≤12, then the area of the region R :

Important Questions on Straight Line

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