Introduction
Homogeneous Equation : A rational, integral, algebraic equation of the variables x and y is said to be homogeneous equation of nth degree in x and y, when the sum of the indices of x and y in every term is the same and is equal to n.
Equations Of StraightLines
A straight line is represented by an equation of the first degree in two variables (x and y). Conversely locus of an equation of the first degree in two variables is a straight line.
Equation Of Line in Point-Slope Form
AB be a straight line passing through B (h, k) with slope m.
Equation of a Line in Two-point Form
Let the line pass through A(x1, y1) and B(x2, y2), the two given points.
Equation of a Line in Slope-intercept Form
LM be the given line with inclination q and intersecting the y-axis at C, so that OC=c.
Equation of a Line in Intercept Form
AB be a line making intercepts OA = a on x-axis and OB = b on y-axis.
Equation of a Line in Normal Form
AB makes intercepts psec a on the x-axis and pcosec a on the y-axis.
Angle Between Two Lines
To find the angle between the lines of the equation.
To Find The Length of the Perpendicular
To find the length of the perpendicular from the point (x1,y1) on the line xcos a + ysin a = p
To Find The Length of the Perpendicular (cont'd..)
To find the length of the perpendicular from the point (x1,y1) on the line xcos a + ysin a = p
To Find The Equation Of the Bisector
To find the equation of the bisectors of the angle between ax+by+c=0 and ax1+by1+c1=0
Point of Intersection of Two lines
Straight lines intersect at (X1,Y1)
Condition for Three Lines to be Concurrent
The condition for the three lines L1= 0, L2= 0 and L3= 0 to be concurrent.
Equation of the line passing through the intersection of two lines
The equation of a line contains two arbitrary constants. This means two geometrical conditions must be given to obtain the equation of a line. If a line passes through the intersection of two lines (given) only one geometrical.
Homogenous equation of second degree in x and y represents a pair of straight lines passing through the origin
To show that a homogenous equation of second degree in x and y represents a pair of straight lines passing through the origin.
A combined equation of the two lines through the origin is a homogenous equation of second degree
To show that a homogenous equation of degree n in x and y represents n straight lines passing through the origin.
Translation of Axes
An equation corresponding to a set of points with reference to a system of coordinate axes may be simplified by taking the set of points in some other suitable coordinate system, such that all geometrical properties remain unchanged. One such transformation is that in which the new axes are transformed parallel to the original axes and origin is shifted to a new point. A transformation of this kind is called a Translation of Axes.
Summary
The equation of a straight line parallel to x-axis and at a distance h from it is given by y = h.
