Page 157 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes If a line with slope m makes x-intercept d. Then equation of the line is y = m (x – d).
x y
Equation of a line making intercepts a and b on the x-and y-axis, respectively, is 1.
a b
The equation of the line having normal distance from origin p and angle between normal
and the positive x-axis is given by x cos + y sin = p .
Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is
called the general linear equation or general equation of a line.
The perpendicular distance (d) of a line Ax + By+ C = 0 from a point (x , y ) is given by
1 1
Ax 1 By 1 C
d .
A 2 B 2
Distance between the parallel lines Ax + By + C = 0 and Ax + By + C = 0, is given by
1 2
C C
d 1 2 .
A 2 B 2

5.7 Keywords

Condition of Parallelism: When two lines are parallel then their inclination are equal.

Condition of Prependicular: Two non-vertical lines are perpendicular to each other of and only
of their slopes are negative reciprocals of each other.
Inclination of line: The angle made by a line with positive direction and measured in anti-clock
-wise.

5.8 Self Assessment

Fill in the blanks:
1. A line in a coardinate plane forms two angles with x-axis, which are ………………

2. If is the inclination of a line than tan is called the ……………… of line
3. Two non-vertical lines are parallel if and only if their slopes are ………………
m m
4. If 2 1 is positive, then tan will be ………………
1 m m
1 2
5. Two non-vertical lines are perpendicular to each of and only of their slopes are
……………… of each other.
Choose the Correct Answer:

6. Equation of line is equals to when point ( 2, 3) & slope 4
(a) 4x + y + 5
(b) 2x + 4y 5

(c) 4x + 2y + 6
(d) 4x + 2y + 3

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