Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 2

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12th Maharashtra Board

IMPORTANT

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If the lines represented by $k x^{2} - 3 x y + 6 y^{2} = 0$ are perpendicular to each other then _____

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Important Questions on Pair of Straight Lines

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 3

Auxiliary equation of

2 x^{2} + 3 x y - 9 y^{2} = 0

is ____

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12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 4

The difference between the slopes of the lines represented by

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

is _____

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 5

If the two lines

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

make angles

α

and

β

, with

X

-axis, then

\tan (α + β) =

_______

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 6

If the slope of one of the two lines

\frac{x^{2}}{a} + \frac{2 x y}{h} + \frac{y^{2}}{h} = 0

is twice that of the other, then ab:

h^{2} =

_____

MEDIUM

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 7

The joint equation of the lines through the origin and perpendicular to the pair of lines

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

is

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 8

If acute angle between lines

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

is,

\frac{π}{4}

then

4 h^{2} =

______

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 9

If the equation

3 x^{2} - 8 x y + q y^{2} + 2 x + 14 y + p = 1

represents a pair of perpendicular lines then the values of

p

and

q

are respectively

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 4 - Pair of Straight Lines>MISCELLANEOUS EXERCISE 4>Q 10

The area of triangle formed by the lines

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

and

x - y - 4 = 0

is _____