Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 13

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Let a line $L_{1} : 3 x + 2 y - 6 = 0$ intersect the $x$ and $y$ axes at $P$ and $Q$ respectively. Let another line $L_{2}$ perpendicular to $L_{1}$ cut the $x$ and $y$ axes at $R$ and $S$ respectively. The locus of point of intersection of the lines $P S$ and $Q R$ is

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Important Questions on Straight Lines

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 14

If the variable line

\frac{x}{α} + \frac{y}{β} = 1

(

α, β

are variables) moves in such a way that

\frac{1}{α^{2}} + \frac{1}{β^{2}} = \frac{1}{m^{2}},

(m is constant)

, then the locus of foot of perpendicular from the origin on the straight line is ?

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 15

A line intersect

x

-axis at

A (4, 0)

and

y

-axis at

B (0, - 3)

. A variable line

P Q

which is perpendicular to

A B

intersects

x

-axis at

P

and

y

-axis at

Q

. If

A Q

and

B P

intersect at

R

, then locus of

R

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 16

Two points

P (2, 0)

and

Q (- 2, 0)

are given.

R

is a variable point on one side of the line

P Q

such that

∠ R P Q - ∠ R Q P

is a positive constant

2 α

. The locus of

R

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 1

If for a line the length of intercept on

x

-axis is

3

and on

y

-axis is

6

. Then which of the followings is/ are true.

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 2

Consider triangle

A B C

where

A = (4, 4), B = (7, 4), C = (4, 7)

then

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 3

The equation of the lines passes through

(2, 3)

and making an angle of

45 °

with the line

2 x - y + 3 = 0

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 4

Consider a point

A (3, 4)

and line

L \equiv x + 3 y + 5 = 0

then

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 5

Which of the following is true ?