Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>EXERCISE 11.4>Q 33

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The co-ordinates of a point $P$ referred to a rectangular co-ordinate system where $O$ is the origin are $(1, - 2)$ . The axes are rotated about $O$ through an angle $θ$ . If the co-ordinates of $P$ in the new system are $(k - 1, k + 1)$ , then $k^{2}$ is equal to

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Important Questions on Straight Lines

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>EXERCISE 11.4>Q 34

Centroid of the triangle, the equations of whose sides are

12 x^{2} - 20 x y + 7 y^{2} = 0

and

2 x - 3 y + 4 = 0

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>EXERCISE 11.4>Q 35

The line joining two points

A (2, 0), B (3, 1)

is rotated about

A

in the counter-clockwise sense through an angle

15 °

. If

B

goes to

C

in the new position, then co-ordinates of

C

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>EXERCISE 11.4>Q 36

The equations of the diagonals of the square formed by the pairs of straight lines

3 x^{2} + 8 x y - 3 y^{2} = 0

and

3 x^{2} + 8 x y - 3 y^{2} + 2 x - 4 y - 1 = 0

are

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>EXERCISE 11.4>Q 37

Keeping the origin fixed, the coordinate axes are rotated through an angle

θ

. If the equation of the line

\frac{x}{a} + \frac{y}{b} = 1

with respect to new axes is

\frac{x}{p} + \frac{y}{q} = 1

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>EXERCISE 11.4>Q 38

The equation of the lines through the origin and which are perpendicular to the pair of straight lines

x^{2} - 3 x y + 2 y^{2} = 0

is

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>EXERCISE 11.4>Q 39

The value of

h

for which

3 x^{2} - 2 h x y + 4 y^{2} = 0

represents a pair of coincident lines are

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 1

Find the inclination of the line

x - y + 3 = 0

with the positive direction of

x -

axis.

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Gamma Question Bank for Engineering Mathematics>Chapter 13 - Straight Lines>Assignment>Q 2

Find the angle between the lines joining the points

(3, - 1) & (2, 3) &

the points

(5, 2)

and

(9, 3)

.