* Alok Kumar is a winner of INDIAN NATIONAL MATHEMATICS OLYMPIAD (INMO-91).
He trains IIT and Olympiad aspirants.DEFINITION
The straight line is a curve such that every point on the
line segment joining any two points on it lies on it.
SLOPE (GRADIENT) OF A LINE
The slope of a line is generally denoted by m. Thus,
m = tanθ
z Slope of line parallel to x-axis is m = tan0° = 0
z Slope of line parallel to y-axis is m = tan90° = ∞
z Slope of the line equally inclined with the axes is
1 or –1.
z Slope of the line through the points A(x 1 , y 1 ) and
B(x 2 , y 2 ) is yy
xx21
21−
−(taken in the same order).z Slope of the line ax + by + c = 0, b ≠ 0 is −a
b
.z Slope of two parallel lines are equal.
z If m 1 and m 2 be the slopes of two perpendicular
lines, then m 1 m 2 = –1.
EQUATION OF STRAIGHT LINE IN DIFFERENT
FORMS
z Slope form : y = mx
z Point slope form : y – y 1 = m(x – x 1 )
z Slope intercept form : y = mx + c
z Intercept form : x
ay
b+= 1z Two point form: Equation of the line
through the points A (x 1 , y 1 ) and B(x 2 , y 2 ) is
()yy yy()
xx− = − xx
−
1 21 −
211
In the determinant form it is given as
xy
xy
xy1
1
111 0
22=z Normal or Perpen-
dicular form : xcosα +
ysinα = p, where p is the
perpendicular distance of
the line from the origin
and α be the angle made
by the perpendicular.
z Symmetrical or Parametric or Distance form of
a line :xx yy− (^11) = − =r
cosθθsin ,
where r is the distance
between the point
P(x, y) and A(x 1 , y 1 ).
This column is aimed at Class XI students so that they can prepare for competitive exams such as JEE Main/Advanced, etc. and
be also in command of what is being covered in their school as part of NCERT syllabus. The problems here are a happy blend
of the straight and the twisted, the simple and the difficult and the easy and the challenging.
*ALOK KUMAR, B.Tech, IIT Kanpur