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

EASY

JEE Main/Advanced

IMPORTANT

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If the equation $12 x^{2} + 7 x y - p y^{2} - 18 x + q y + 6 = 0$ represents two perpendicular lines, then the value of $p$ and $q$ are :

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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 4

If the angle between the two lines represented by

2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0

is

\tan^{- 1} m,

then

m =

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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

The equation of second degree

x^{2} + 2 \sqrt{2} x y + 2 y^{2} + 4 x + 4 \sqrt{2} y + 1 = 0

represents a pair of straight lines. The distance between them is

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 1

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

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 :