Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 40

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In an isosceles triangle $A B C$ , the coordinate of the points $B$ and $C$ on the base $B C$ are respectively $(1, 2)$ and $(2, 1)$ . If equation of line $A B$ is $2 x - y = 0$ , then slope of line $A C$ is

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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 41

The number of lines which pass through the point

(2, - 3)

and are at distance

7

units from point

(- 1, 2)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 42

The line

2 x + 3 y = 12

meet the

x

-axis at

A

and

y

-axis at

B

. The line through

(5, 5)

perpendicular to

A B

meets the

x

-axis,

y

-axis and the given line at

C, D

and

E

respectively. If

O

is the origin of coordinates, then three times the area of

O C E B

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 43

Locus of the points which are at equal distances from $3 x + 4 y - 11 = 0$ and $12 x + 5 y + 2 = 0$ and which is near to the origin is $a x + b y - 133 = 0$ then $a + b$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 44

The distance between the pair of parallel lines $x^{2} + 2 x y + y^{2} - 8 a x - 8 a y - 9 a^{2} = 0$ is $(k a)$ units then $k^{2}$ is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 45

If

(a + 3 b) (3 a + b) = 4 h^{2}

, then the angle between the lines represented by

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

is

θ

then the value of

\sec^{2} θ + 5 \cot^{2} \frac{θ}{2}

is equal to

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

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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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?