Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 92

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Consider a triangle $A B C,$ whose vertices are $A (- 2, 1), B (1, 3)$ and $C (x, y) .$ If $C$ is a moving point such that area of $Δ A B C$ is constant, then locus of $C$ is

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Important Questions on Point and Straight Line

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 93

If the equation of the locus of a point equidistant from the points

(a_{1}, b_{1})

and

(a_{2}, b_{2})

is

(a_{1} - a_{2}) x + (b_{1} - b_{2}) y + c = 0

, then the value of

c

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 94

The equation of bisectors of two lines

L_{1} & L_{2}

are

2 x - 16 y - 5 = 0

and

64 x + 8 y + 35 = 0 .

If the line

L_{1}

passes through

(- 11, 4),

the equation of acute angle bisector of

L_{1} & L_{2}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 95

The equation of the internal bisector of

∠ B A C

of

Δ A B C

with vertices

A (5, 2), B (2, 3)

and

C (6, 5)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 96

Equation of bisector of the angle between two lines

3 x - 4 y + 12 = 0

and

12 x - 5 y + 7 = 0

which contains a point

(- 1, 4)

in its region is :

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 97

The least positive value of

t

, so that the lines

x = t + α, y + 16 = 0

and

y = α x

are concurrent, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 98

Consider the family of lines

5 x + 3 y - 2 + λ_{1} (3 x - y - 4) = 0

and

x - y + 1 + λ_{2} (2 x - y - 2) = 0

. Equation of a straight line that belongs to both families is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 99

The equation of a line of the system

2 x + y + 4 + λ (x - 2 y - 3) = 0

which is at a distance

\sqrt{10}

units from point

A (2, - 3)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 100

The line

a x + b y + c = 0

, where

3 a + 2 b + 4 c = 0

is concurrent at the point