Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 36

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Two fixed points $A$ and $B$ have co-ordinates $(x_{1}, y_{1})$ and $(x_{2}, y_{2}) .$ A point $P$ moves such that $A P$ is perpendicular to $B P$ , then locus of $P$ 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 37

Locus of the middle point of the intercept on the line

y = x + c

made by the lines

2 x + 3 y = 5

and

2 x + 3 y = 8, c

being a parameter, 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 39

The area of a triangle formed by line

L

and coordinate axes is

7

square units, if the equation of line

L

is

x + 5 y = λ

then

λ^{2}

is equal to

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

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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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 -