EASY

JEE Main/Advanced

IMPORTANT

Earn 100

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 $x$ .

Important Questions on Pair of Straight Lines

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

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 5

The equation of the line joining the origin to the point of intersection of the lines

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

is :

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

Find the equation of the lines joining the origin to the points of intersection of

3 x - 2 y = 1

with

3 x^{2} + 5 x y - 3 y^{2} + 2 x + 3 y = 0

and show that they are at right angles.

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

If the straight line joining the origin and the points of intersection of

y = m x + 1

and

x^{2} + y^{2} = 1

be perpendicular to each other, find the value of

m

Find the area of the triangle formed by the lines represented by ax2+2hxy+by2+2gx+2fy+c=0 and axis of x.

Important Questions on Pair of Straight Lines

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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 $x$ .