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

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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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Important Questions on Straight Lines

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 11

Let a given line

L_{1} (a x + b y + c = 0)

intersects the

x

and

y

axes at

P

and

Q

respectively. Let another line

L_{2}

perpendicular to

L_{1}

cuts the axes at

R

and

S

respectively. Find the locus of the point of intersection of the lines

P S

and

Q R

.

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 12

Vertices of a triangle are

A (x_{1}, x_{1} \tan α_{1}), B (x_{2}

,

x_{2} \tan α_{2})

and

C (x_{3}, x_{3} \tan α_{3})

. If the circumcentre coincides with the origin and the orthocentre

H = (\bar{x}, \bar{y})

, Then which of the following is necessarily true?