TopSpace Analytical Geometry is similar to the Algebra which is used for geometric objects such as points, straight line, circle, planes, second order curves and surfaces. The main principles of analytic geometry are based on method of coordinates and the methods of elementary algebra. The method of coordinates is linked with the intense development.
The principal method of coordinates is given below:
Suppose we have two mutual perpendicular straight lines ‘Gx’ and ‘Hy’ in a plane ‘⊼’. These lines are according to their direction, and the coordinate origin ‘o’ and selected scale unit ‘r’, this is said to be Cartesian orthogonal system ‘Pxy’ are the coordinates which lie on the plane. We take two straight lines, these lines are known as Abscissa or we can say the axis and the Ordinate axis respectively and the Straight Line is represented by an algebraic equation and the algebraic equation is of order 1.
So the equation is:
Px + Qy + R = 0;
The curves of the second order are represented by another equation which is given below:
=> Px2 + Qxy + Ry2 + Sx + Ty + U = 0;
These all are the examples of analytic geometric.
The points are denoted as Ordered Pair in the space analytic geometric and in the case of straight line; it is denoted as Set of points which satisfy the linear equation and the part of analytic geometry which deals with the linear equation is known as linear algebra. The other name of analytic geometry is coordinate geometry, Cartesian geometry. Analytic geometry is based on the coordinate system and the principles of algebra and analysis.
Now we will see how to find the distance and angle in analytic geometry:
Suppose we have coordinates s1, s2 and t1, t2 for the plane of geometry:
We will see how to find the distance of plane of analytic geometry by using above coordinates:
d = √ (s2 - s1)2 + (t2 - t1)2; Where‘d’ is distance.
By pythagoras theorem we can find the distance in analytic geometry;