- RD Chapter 23- The Straight Lines Ex-23.1
- RD Chapter 23- The Straight Lines Ex-23.2
- RD Chapter 23- The Straight Lines Ex-23.3
- RD Chapter 23- The Straight Lines Ex-23.4
- RD Chapter 23- The Straight Lines Ex-23.5
- RD Chapter 23- The Straight Lines Ex-23.6
- RD Chapter 23- The Straight Lines Ex-23.7
- RD Chapter 23- The Straight Lines Ex-23.8
- RD Chapter 23- The Straight Lines Ex-23.9
- RD Chapter 23- The Straight Lines Ex-23.10
- RD Chapter 23- The Straight Lines Ex-23.11
- RD Chapter 23- The Straight Lines Ex-23.12
- RD Chapter 23- The Straight Lines Ex-23.13
- RD Chapter 23- The Straight Lines Ex-23.14
- RD Chapter 23- The Straight Lines Ex-23.15
- RD Chapter 23- The Straight Lines Ex-23.16
- RD Chapter 23- The Straight Lines Ex-23.17
- RD Chapter 23- The Straight Lines Ex-23.19

RD Chapter 23- The Straight Lines Ex-23.1 |
RD Chapter 23- The Straight Lines Ex-23.2 |
RD Chapter 23- The Straight Lines Ex-23.3 |
RD Chapter 23- The Straight Lines Ex-23.4 |
RD Chapter 23- The Straight Lines Ex-23.5 |
RD Chapter 23- The Straight Lines Ex-23.6 |
RD Chapter 23- The Straight Lines Ex-23.7 |
RD Chapter 23- The Straight Lines Ex-23.8 |
RD Chapter 23- The Straight Lines Ex-23.9 |
RD Chapter 23- The Straight Lines Ex-23.10 |
RD Chapter 23- The Straight Lines Ex-23.11 |
RD Chapter 23- The Straight Lines Ex-23.12 |
RD Chapter 23- The Straight Lines Ex-23.13 |
RD Chapter 23- The Straight Lines Ex-23.14 |
RD Chapter 23- The Straight Lines Ex-23.15 |
RD Chapter 23- The Straight Lines Ex-23.16 |
RD Chapter 23- The Straight Lines Ex-23.17 |
RD Chapter 23- The Straight Lines Ex-23.19 |

Find the equation of the straight lines passing through the origin andmaking an angle of 45^{o} with the straight line √3x + y = 11.

**Answer
1** :

Given:

Equation passesthrough (0, 0) and make an angle of 45° with the line √3x + y = 11.

We know that, theequations of two lines passing through a point x1,y1 and making anangle α with the given line y = mx + c are

Find the equations to the straight lines which pass through the originand are inclined at an angle of 75^{o} to the straight line x + y+ √3(y – x) = a.

**Answer
2** :

Given:

The equation passesthrough (0,0) and make an angle of 75° with the line x + y + √3(y – x) = a.

We know that theequations of two lines passing through a point x1,y1 and making anangle α with the given line y = mx + c are

**Answer
3** :

Given:

The equation passesthrough (2,-1) and make an angle of 45° with the line 6x + 5y – 8 = 0

We know that theequations of two lines passing through a point x_{1}, y_{1} andmaking an angle α with the given line y = mx + c are

Here, equation of thegiven line is,

6x + 5y – 8 = 0

5y = – 6x + 8

y = -6x/5 + 8/5

Comparing thisequation with y = mx + c

We get, m = -6/5

Where, x_{1} =2, y_{1} = – 1, α = 45°, m = -6/5

So, the equations ofthe required lines are

x + 11y + 9 = 0 and11x – y – 23 = 0

∴ The equation of givenline is x + 11y + 9 = 0 and 11x – y – 23 = 0

**Answer
4** :

Given:

The equation passesthrough (h, k) and make an angle of tan^{-1} m with theline y = mx + c

We know that theequations of two lines passing through a point x_{1}, y_{1} andmaking an angle α with the given line y = mx + c are

m′ = m

So,

Here,

x_{1} =h, y_{1} = k, α = tan^{-1} m, m′ = m.

So, the equations ofthe required lines are

**Answer
5** :

Given:

The equation passesthrough (2, 3) and make an angle of 45^{0}with the line 3x + y – 5= 0.

We know that theequations of two lines passing through a point x1,y1 and making anangle α with the given line y = mx + c are

Here,

Equation of the givenline is,

3x + y – 5 = 0

y = – 3x + 5

Comparing thisequation with y = mx + c we get, m = – 3

x_{1} =2, y_{1} = 3, α = 45∘, m = – 3.

So, the equations ofthe required lines are

x + 2y – 8 = 0 and 2x– y – 1 = 0

∴ The equation of givenline is x + 2y – 8 = 0 and 2x – y – 1 = 0

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