Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 30

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Three vertices of triangle $A B C$ are $A (- 1, 11), B (- 9, - 8)$ and $C (15, - 2)$ . The equation of angle bisector of angle $A$ is-

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Important Questions on Point and Straight Line

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 31

Given the four lines with the equations

$x + 2 y - 3 = 0, 3 x + 4 y - 7 = 0$

$2 x + 3 y - 4 = 0, 4 x + 5 y - 6 = 0$

then

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 32

The co-ordinates of the point of reflection of the origin

(0, 0)

in the line

4 x - 2 y - 5 = 0

is

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 33

If the axes are rotated through an angle of

30 °

in the anti-clockwise direction, the coordinates of point

(4, - 2 \sqrt{3})

with respect to new axes are-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 34

If one diagonal of a square is along the line

x = 2 y

and one of its vertex is

(3, 0)

, then its sides through this vertex are given by the equations-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 35

The line

(p + 2 q) x + (p - 3 q) y = p - q

for different values of

p

and

q

passes through a fixed point whose co-ordinates are-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 36

The equation

2 x^{2} + 4 x y - p y^{2} + 4 x + q y + 1 = 0

will represent two mutually perpendicular straight lines, if-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 37

Equation of the pair of straight lines through origin and perpendicular to the pair of straight lines

5 x^{2} - 7 x y - 3 y^{2} = 0

is

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 38

If the straight lines joining the origin and the points of intersections of the curve

5 x^{2} + 12 x y - 6 y^{2} + 4 x - 2 y + 3 = 0

and

x + k y - 1 = 0

are equally inclined to the co-ordinate axis, then the value of

k

-