Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.4>Q 1

EASY

JEE Main/Advanced

IMPORTANT

Earn 100

Find the area of the parallelogram formed by the lines
$2 x^{2} + 5 x y + 3 y^{2} = 0$ and $2 x^{2} + 5 x y + 3 y^{2} + 3 x + 4 y + 1 = 0$

Important Questions on Pair of Straight Lines

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.4>Q 2

Find the locus of the incentre of the triangle formed by

x y - 4 x - 4 y + 16 = 0

and

x + y = a

(

a > 4, a \neq 4 \sqrt{2}

and

a

is the parameter)

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.4>Q 3

If the equation

2 h x y + 2 g x + 2 f y + c = 0

represents two straight lines, show that they form a rectangle of area

\frac{|f g|}{h^{2}}

with the co-ordinate axes.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.4>Q 4

Find the area of the triangle formed by the lines represented by

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

and axis of

x

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.4>Q 5

Find the equations of the straight lines passing through the point

(1, 1)

and parallel to the lines represented by the equation

x^{2} - 5 x y + 4 y^{2} + x + 2 y - 2 = 0

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.5>Q 1

If the straight lines joining origin to the points of intersection of the line

x + y = 1

with the curve

x^{2} + y^{2} + x - 2 y - m = 0

are perpendicular to each other, then the value of

m

should be :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.5>Q 2

The pair of straight lines joining the origin to the common points of

x^{2} + y^{2} = 4

and

y = 3 x + c

are perpendicular, if

c^{2} =

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.5>Q 3

Mixed term

x y

is to be removed from the general equation of second degree

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

, one should rotate the axes through an angle

θ

, then

\tan 2 θ

is equal to :

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 3 - Pair of Straight Lines>INTRODUCTORY EXERCISE 3.5>Q 4

Combined equation of line joining the origin to the points of intersection of

2 x^{2} + 3 x y - 4 x + 1 = 0

and

3 x + y = 1

is given by