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

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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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Important Questions on Straight Lines

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 34

A variable straight line passes through the points of intersection of the lines

x + 2 y = 1

and

2 x - y = 1

and meets the co-ordinate axes in

A

and

B

. The locus of middle point of

A B

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 35

If

A (\cos α, \sin α), B (\sin α, - \cos α), C (2, 1)

are vertices of a triangle

A B C

. The locus of its centroid if

α

varies is

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

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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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