Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 11

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

Let a given line $L_{1} (a x + b y + c = 0)$ intersects the $x$ and $y$ axes at $P$ and $Q$ respectively. Let another line $L_{2}$ perpendicular to $L_{1}$ cuts the axes at $R$ and $S$ respectively. Find the locus of the point of intersection of the lines $P S$ and $Q R$ .

33.33% studentsanswered this correctly

Important Questions on Straight Lines

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 12

Vertices of a triangle are

A (x_{1}, x_{1} \tan α_{1}), B (x_{2}

,

x_{2} \tan α_{2})

and

C (x_{3}, x_{3} \tan α_{3})

. If the circumcentre coincides with the origin and the orthocentre

H = (\bar{x}, \bar{y})

, Then which of the following is necessarily true?

MEDIUM

JEE Main/Advance

IMPORTANT

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

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

MEDIUM

JEE Main/Advance

IMPORTANT

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 ?

MEDIUM

JEE Main/Advance

IMPORTANT

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

MEDIUM

JEE Main/Advance

IMPORTANT

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

EASY

JEE Main/Advance

IMPORTANT

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.

EASY

JEE Main/Advance

IMPORTANT

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

MEDIUM

JEE Main/Advance

IMPORTANT

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