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 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 - Straight Lines>Assignment>Q 26

The mid-point of line segment joining

(3, - 1)

and

(1, 1)

is shifted by two units (in the sense of increasing

y

) perpendicular to the line segment. Then, the coordinates of the point in the new position are

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 27

Distance between the pair of straight lines

x^{2} + 6 x y + 9 y^{2} + 4 x + 12 y - 5 = 0

is given by

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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 29

Two ends

A & B

of a straight line segment of constant length

c

slide upon the fixed rectangular axes

O X & O Y

respectively. If the rectangle

O A P B

is completed. Then, find the locus of the foot of the perpendicular drawn from

P

to

A B

.

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 31

A variable straight line, drawn through the point of intersection of the straight line

\frac{x}{4} + \frac{y}{2} = 1

and

\frac{x}{2} + \frac{y}{4} = 1

meets the co-ordinate axes in

A

and

B

. The locus of midpoint of

A B

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 33

y = m x

be a variable line (

m

is variable) intersect the lines

2 x + y - 2 = 0

and

x - 2 y + 2 = 0

in

P

and

Q

. The locus of midpoint of segment of

P Q

. is