Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 1

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If the sides of triangle $A B C$ are such that $a = 4$ , $b = 5, c = 6$ then the ratio in which excentre corresponding to $A$ divides the angle bisector $A D$ in the ratio

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Important Questions on Straight Lines

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 3

Line

a x + b y + p = 0

makes angle

\frac{π}{4}

with

x \cos α + y \sin α = p, p \in R^{+}

. If these lines and the line

x \sin α - y \cos α = 0

are concurrent, then:

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 4

The equation of three lines

P Q, R S

and

L M

are

(p - q) x + (q - r) y + (r - p) = 0, (q - r) x + (r - p) y + (p - q) = 0

and

(r - p) x + (p - q) y + (q - r) = 0

respectively. Which one of the following inferences is correct?

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 5

The equation

\sqrt{(x^{2} + 4 y^{2} - 4 x y + 4)} + x - 2 y = 1

represents a/an

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 6

The equation of lines joining $(0,0)$ and points of intersection of

x^{2} + y^{2} + 2 x y = 4, 3 x^{2} + 5 y^{2} - x y = 7

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 7

If two lines represented by

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

bisect the angle between the other two, then the value of

c

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 8

The equation of a pair of straight lines is

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

. The axes are rotated by angle

ϕ

so that term containing

x y

in the equation may be removed, Then

ϕ

must be equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 9

If one equation

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

represents a pair of straight lines, then the product of the distances of the lines from origin is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 10

The line

A B

whose equation is

x - y = 2

cuts the

x

-axis at

A

and

B

is

(4, 2)

. The line segment

A B

is rotated about

' A'

through an angle

45 °

in the anticlockwise sense. Then the equation

A B

in new position is