Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 88

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Find locus of centroid of $Δ A B C,$ if $B (1, 1), C (4, 2)$ and $A$ lies on the line $y = x + 3$

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Important Questions on Point and Straight Line

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 89

The locus of the midpoint of the distance between the axes of the variable line

x \cos α + y \sin α = p,

where

p

is constant, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 90

Find the locus of a point which moves so that sum of the squares of its distance from the axes is equal to

3

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 91

A variable straight line passes through a fixed point

(a, b)

intersecting the coordinate axes at

A

and

B

. If

O

is the origin, then locus of centroid of triangle

O A B

is:

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

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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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 :