Classical analytic geometry is an important branch of mathematics, which mainly studies the positional relationship of points, lines and surfaces in plane and space and their changing laws. In the field of mathematics, classical analytic geometry has a wide range of applications.

First of all, classical analytic geometry has important applications in geometry. For example, it can help us understand and solve some complex geometric problems, such as solving the area and perimeter of a triangle. In addition, classical analytic geometry can also be used to study the properties of curves, such as curvature and inflection point.

Secondly, classical analytic geometry also has important applications in algebra. For example, it can help us understand and solve some complex algebraic equations. In addition, classical analytic geometry can also be used to study the properties of vector space, such as linear transformation and matrix operation.

Thirdly, classical analytic geometry also has important applications in physics. For example, it can help us understand and solve some complex physical problems, such as electromagnetic field and gravitational field. In addition, classical analytic geometry can also be used to study the trajectory of moving objects, such as parabolic motion and circular motion.

Finally, classical analytic geometry also has important applications in computer science. For example, it can help us to understand and solve some complex computer graphics problems, such as 3D modeling and animation. In addition, classical analytic geometry can also be used to study problems in computer vision, such as image processing and pattern recognition.