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

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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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Important Questions on Straight Lines

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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 1

If for a line the length of intercept on

x

-axis is

3

and on

y

-axis is

6

. Then which of the followings is/ are true.

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 2

Consider triangle

A B C

where

A = (4, 4), B = (7, 4), C = (4, 7)

then

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 28

The point of intersection of the straight line

3 x + 5 y = 1

and

(2 + c) x + 5 c^{2} y = 1

where

c \neq 1

and

- \frac{3}{2}

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 32

A straight line passes through a fixed point

(2, 3)

. Locus of the foot of the perpendicular on it drawn from the origin is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 38

If the pair of straight lines

x^{2} - y^{2} + 2 x + 1 = 0

meet the

y

-axis in

A

and

B, | A B |

equals to

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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?

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 14

If the variable line

\frac{x}{α} + \frac{y}{β} = 1

(

α, β

are variables) moves in such a way that

\frac{1}{α^{2}} + \frac{1}{β^{2}} = \frac{1}{m^{2}},

(m is constant)

, then the locus of foot of perpendicular from the origin on the straight line is ?