Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 17

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The equation of a straight line equally inclined to the axes and equidistant from the points $(1, - 2)$ and $(3, 4)$ 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 18

A line passing through

(0, 0)

and perpendicular to

2 x + y + 6 = 0, 4 x + 2 y - 9 = 0

then the origin divides the line in the ratio of

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 19

A ray of light is sent along the line

x - 2 y - 3 = 0

on reaching the line

3 x - 2 y - 5 = 0

the ray is reflected from it, then the equation of the line containing the reflected ray is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 20

The equation of the bisector of the acute angle between the lines

3 x - 4 y + 7 = 0

and

12 x + 5 y - 2 = 0

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 21

If

a, b

and

c

are in

A . P .

then

a x + b y + c = 0

will always pass through a fixed point whose co-ordinates are

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 22

The possible value of

λ

for which the following three lines

x + y = 1, λ x + 2 y = 3, λ^{2} x + 4 y + 9 = 0

are concurrent is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 24

The straight line

a x + b y = 1

makes with the curve

p x^{2} + 2 a x y + q y^{2} = r

a chord which subtends a right angle at the origin. Then

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 25

The straight lines joining the origin to the point of intersection of two curves

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

and

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

will be at right angles to one another if

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Conic Section>EXERCISE 13.5>Q 47

The equation

2 x^{2} + 3 y^{2} - 8 x - 18 y + 35 = k

represents