OP Malhotra Class-11 **The Straight Line **S.Chand ISC Maths Solutions Chapter-16. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-16 (a), 16 (b), 16 (c), 16 (d), 16 (e), 16 (f), 16 (g), 16 (h), 16 (i), 16 (j), With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Class: | 11th |

Subject: | Mathematics |

Chapter : | Ch-16 The Straight Line of Section -A |

Board | ISC |

Writer | OP Malhotra |

Publications | S.Chand Publications 2020-21 |

-: Select Topics :-

### OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

**Straight Line**

Any curve is said to be a straight line if two points are taken on the curve such that every point on the line segment joining any two points on it lies on the curve. General equation of a line is ax + by + c = 0.

**Various Forms of the Equation of a Line**

If a line is at a distance k and parallel to X-axis, then the equation of the line is y = ± k.

If a line is parallel to Y-axis at a distance c from Y-axis, then its equation is x = ± c.

Slope-intercept form: The equation of line with slope m and making an intercept c on the y-axis, is y = mx + c.

One point-slope form: The equation of a line which passes through the point (x_{1}, y_{1}) and has the slope of m is given by y – y_{1} = m (x – x_{1}).

**Position of Points is Relative to a Given Line**

Let the equation of the given line be ax + by + c = 0 and let the coordinates of the two given points be P(x_{1}, y_{1}) and Q(x_{2}, y_{2}).

The two points are on the same side of the straight line ax + by + c = 0, If ax_{1} + by_{1} + c and ax_{2} + by_{2} + c have the same sign.

The two points are on the opposite sides of the straight line ax + by + c = 0, If ax_{1} + by_{1} + c and ax_{2} + by_{2} + c have opposite sign.

**Condition of concurrency for three given lines**

a_{1}x + b_{1}y + c_{1} = 0, a_{2}x + b_{2}y + c_{2} = 0 and a_{3}x + b_{3}y+ c_{3} = 0 is a_{3}(b_{1}c_{2} – b_{2}c_{1}) + b_{3}(a_{2}c_{1} – a_{1}c_{2}) + c_{3}(a_{1}b_{2} – a_{2}b_{1}) = 0

**Slope of a Line**

Tan θ is called the slope or gradient of line l if θ is the inclination of a line l. The slope of a line whose inclination is not equal to 90^{0}. It is denoted by ‘m’.

Thus, m = tan θ, θ ≠ 90°

If the slope of the y-axis is not defined, it is observed that the slope of the x-axis is zero.

Exe-16 (a)

### OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-4 to 16-5

### Exe-16 (b)

OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-10 to 16-11

Exe-16 (c)

### Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-14

### Exe-16 (d)

OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-18 to 16-19

Exe-16 (e)

### OP Malhotra The Straight Line S.Chand ISC Maths Solutions

Page 16-21

### Exe-16 (f)

OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-23 to 16-24

Exe-16 (g)

### Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-27

### Exe-16 (h)

OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-29 to 16-30

Exe-16 (i)

### OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-32

### Exe-16 (j)

Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-34

Chapter Test

### OP Malhotra Class-11 The Straight Line S.Chand ISC Maths Solutions

Page 16-38

-: End of **The Straight Line** Solution :-

Return to :- OP Malhotra S. Chand ISC Class-11 Maths Solutions

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