Analytic Geometry Analytic Geometry An analytic geometry is also similar to the algebra which is used model the geometric objects, and the geometric objects are points, straight line, and circle. Points are represented as order pair in the plane analytic geometric and in the case straight line it is represented as set of points which satisfy the linear equation and the part of analytic geometric which deal with the linear equation is said to be linear algebra. Coordinate geometry, Cartesian geometry are all the other name of analytic geometry. And this plane analytic geometry is based on the coordinate system and the principal of algebra and analysis. Now we will see the basic principal of plane analytic geometry which is given below: Every point in the analytic geometry is having a pair of real number coordinates. Cartesian coordinates system is one of the most important in the coordinate system in the plane analytic geometry, where all the x coordinates represented the horizontal position in the graph and y coordinates represented the vertical position in the graph.These coordinates are generally written in the form of order pair (x, y). This analytic geometry can also use for three dimensional geometry, where all the point are represented by an order pair of coordinates like (x, y, z);
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Now we will see how to find the distance and angle of analytic geometry: Let we have coordinates u1, u2 and v1, v2 for the plane of geometry: Then we see how to find the distance of plane of analytic geometry by using above coordinates: d = √ (u2 - u1)2 + (v2 - v1)2; Where d is distance. This distance can be solved by using the Pythagoras theorem; Now we find the angle of plane of geometry: The angle of geometry is: ∅ = arc tan (m); Where m is the slope of line; By using this formula we can find the distance of analytic geometric. Now we will see the intersection in the analytic geometry: Intersection can easily extend to higher dimensions. Let we have two geometric objects U and v which is represented by the relation U (x, y) and V (x, y). We can easily say that the intersection is the group of points (x, y).The intersection of U and V can be solving by the simultaneous equations: Let we have two equations:
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⇒ u2 + v2 = 1; ⇒ (u – 1)2 + v2 = 1; Now we will use the substation method for solving the given equations: First we solve the equation for ‘v’ in terms of ‘u’ then substitute the value of y in the second equation: ⇒ u2 + v2 = 1; ⇒ v2 = 1 – u2; Now put the value of v2 in the second equation :- On putting the value in the second equation we get :⇒ (u – 1)2 + v2 = 1; ⇒ (u – 1)2 + 1 – u2 = 1; Now solve this equation for u :- So we can write the above equation as: ⇒ u2 – 2u + 1 + 1 – u2 = 1; On further solving we get: ⇒ -2u = -1; ⇒ u = ½;
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