1 Slope of a line :
The tangent of angle that al line makes with + ve direction of the x- axis in the anticlockwise sense is called slope of the x- axis in the anticlockwise sense is called slope or gradient of line and is generally denoted by m. thus m = tan q
(i) Slope of line || to x-axis is m =0
(ii) Slope of line || to y-axis is m = ¥ (not defined)
(iii) Slope of the line equally inclined with the axes is 1 or – 1
(iv) Slope of the line throught the point A(x1, y1) and B (x2 , y2) is (y2-y1)/(x2 - x1)
(v) Slope of the line ax + by + c = 0, b ¹ 0 is – (a/b)
(vi) Slope of two parallel lines are equal .
(vii) Is m1 & m2 are slope of two ^ lines then m1m2=-1
2 Standard form of the equation of line :
(i) Equation of x-axis is y =0
(ii) Equation of y-axis is =0
(iii) Equation of a straight line || to x-axis at a distance b form it is y = b
(iv) Equation of a straight line || to y-axis at a distance a from it is x=a
(v) Slope form : Equation of a line through the origin and having slope m is y = mx
(vi) Slope Intercept form : Equation of a line with slope m and making an intercept c on the y-axis is y= mx + c
(vii) Point slope form : Equation of a line with slope m and passing through the point (x1 , y1) is y-y1 = m(x-x1)
(viii) Two point form : Equation of a line passing through the point (x1 , y1) & (x2, y2) is
(ix) Intercept form : Equation of a line making intercepts a and b respectively on x-axis and y-axis is (x/a) + y/b) = 1
(x) Parametric or distance or symmetrical form of the line: Equation of a line passing through (x1 , y1) and making an angle q , 0 £ q £ p , q ¹ (p/2) with the + ve direction of x-axis is
Þ x = x1 + r cos q , y = y1 + r sin q
Where r is the distance of any point P(x,y) on the line from the point (x1 , y1)
(xi) Normal or Perpendicular form : Equation of a line such that the length of the perpendicular from the origin on it is p and the angle which the perperdicular makes with the + ve direction of x-axis is a is x cos a + y sin a = p
3 Angle between two lines :
(i) Two lines a1 x + b1y + c1 = 0 & a2x + b2y + c2 = 0 are
(a) parallel if (a1/a2) = (b1/b2) ¹ (c1 / c2
(b) perpendicular if a1a2 + b1b2 = 0
(c) Identical or coincident if (a1 / a2) = (b1 / b2) = (c1 / c2)
(d) if not above three , then q = tan-1 
(ii) Two lines y = m1 x+ c and y = m2 x + c are
(a) parallel if m1 = m2
(b) perpendicular if m1m2 = -1
(c) If not above two , then q = tan-1 
4 Position of a with respect to a straight line :
The line L(x1, y1) I = 1,2 will be of same sing or of opposite sign according to the point A(x1, y1) & B(x2, y2 ) line on same side or on opposite of L(x,y) respectively .
5 Equation of a line parallel:Equation of a line parallel (or perpendicular ) to the line
Ax + by + c = 0 is ax + by + c = 0 (or bx - ay + l = 0)
6 Equation of st:Equation of st. line through (x1, y1) making an angle a with y = mx + c is 
7 Length of perpendicular:Length of perpendicular from (x1, y1) on ax + by + c = 0 
8 Distance between two parallel lines:Distance between two parallel lines ax + by + c1 = 0
9 Condition of concurrency for three straight lines :
Li º aix + biy + ci = 0 , i = 1,2,3,is
10 Equation of Bisectors of angles between two lines :
11 Family of straight lines :
The general equation of family of straight line will be written in one parameter
The equation of straight line which passes through point of intersection of two given lines L1 and L2 can be taken as L1 + lL2 = 0
12 Homogeneous equation :
If y = m1x and y = m2X be the two equation represented by ax2 + 2hxy + by2 = 0 , then m1 + m2 = -2h/b and m1m2 = a/b
13 General equation of second degree:
Ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represent a pair of 
If y = m1x + c & y = m2x + c represents two straight lines then m1 + m2 = (-2h / b) , m1m2 = (a/b)
14 Angle between pair of straight lines :
The angle between the lines represented by ax2 + 2hxy + by2 + 2gx + 2fy + c= 0 or ax2 + 2hxy + by2 = 0 
(i) The two lines given by ax2 + 2hxy + by2 = 0 are
(a) parallel and coincident iff h2 - ab =0
(b) perpendicular iff a+ b = 0
(ii) The two line given by ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 are
(a) parallel if h2 - ab = 0 & af2 = bg2
(b) perpendicular iff a + b = 0
(c) Coincident iff g2 - ac = 0
15 Combined equation of angle bisector:,Combined equation of angle bisector of the angle between the lines ax2 + 2hxy + by2 = 0 is 
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