Analytical geometry is an essential topic in the JEE Advanced syllabus. It deals with the study of geometry using algebraic equations and coordinates. 

In this topic, students will learn how to solve problems related to lines, planes, circles, and conic sections using algebraic methods.

You should have a strong understanding of algebraic equations and coordinate geometry to excel in analytical geometry. 

Subjects in Analytical Geometry for JEE Advanced Preparation

The Joint Entrance Examination (JEE) Advanced is a highly competitive exam for admission to undergraduate engineering programs in India's premier institutes. Mathematics is one of the three main subjects in the JEE Advanced exam and carries significant weight. One of the essential topics in mathematics is Coordinate Geometry is an essential topic in mathematics. Here are some essential subtopics for JEE Advanced:

Straight Lines

Straight lines are the most fundamental concept in coordinate geometry, forming the foundation for the more advanced topics that follow. A line is a straight path extending infinitely in both directions. One of the essential concepts in straight lines is the slope of a line, which is the ratio of the change in y to the change in x. Another crucial concept is the angle between two lines, which is the angle formed by two lines intersecting. It is necessary to be comfortable with concepts such as the distance between two parallel lines, the point of intersection of two lines, and the equation of a line in different forms.

Circles

Circles are another fundamental concept in coordinate geometry, and their understanding is crucial for solving advanced problems. A circle is a set of points in a plane equidistant from a fixed point called the centre. The standard equation of a circle is (x-a)^2+(y-b)^2=r^2, where (a,b) is the centre of the circle and r is the radius. It is essential to be comfortable with concepts like the equation of a tangent and normal to a circle, which are lines that intersect the circle at exactly one point. Similarly, the equation of a chord and the diameter of a circle are important concepts essential to be comfortable with. Another important concept is the intersection of a line and a circle, which involves finding the points where a line intersects a circle.

Conic Sections

Conic sections are the next level of complexity in coordinate geometry, and their understanding is essential for solving more advanced problems. A conic section is defined as the intersection of a plane with a cone. The three types of conic sections are the parabola, ellipse, and hyperbola. Knowing the standard equation, vertex, focus, directrix, and various equation forms is essential for a parabola. Similarly, for an ellipse, you should know the standard equation, centre, major and minor axis, foci, and eccentricity. For a hyperbola, you should be comfortable with the ordinary equation, centre, foci, vertices, asymptotes, and eccentricity.

Three-Dimensional Geometry

Three-dimensional geometry is an advanced topic in coordinate geometry, requiring a good understanding of the basics. It involves the study of points, lines, and planes in three-dimensional space. One of the essential concepts in three-dimensional geometry is the distance between two points in space, which is calculated using the distance formula. It is also necessary to know the equation of a plane in different forms, such as the standard form, slope-intercept form, and point-normal form. Another crucial concept is the angle between two planes, formed by the intersection of two planes. It is also necessary to know the distance of a point from a plane, which involves finding the shortest distance between a point and a plane.

In conclusion, coordinate geometry is an essential topic in mathematics for JEE Advanced, and you should focus on the subtopics mentioned above to excel in this exam. You should practice solving different types of problems to gain proficiency in these topics and be able to apply the concepts to solve complex problems.

Analytical Geometry for JEE Advanced Preparation: Tips

• Preparing for analytical geometry in JEE Advanced requires a strong understanding of the concepts and a lot of practice. Here are some tips to help you with your preparation:
• Master the basics: Before diving into more complex problems, ensure you have a solid understanding of the basics of analytical geometry. This includes understanding the standard equations of lines, circles, and conic sections, as well as the properties and characteristics of each.
• Practice regularly: Analytical geometry requires a lot of practice to master. Exercise solving problems regularly to build your skills and speed.
• Develop a problem-solving approach: Analytical geometry problems can be complex and multi-step. Develop a problem-solving approach that works for you, such as breaking down the problem into smaller parts or using diagrams to visualise the problem.
• Understand the inter-relationships: Analytical geometry concepts are often interconnected. Ensure you understand how the concepts relate and can be used together to solve problems.
• Learn to use calculus: Calculus plays a role in many analytical geometry problems in JEE Advanced. Ensure you are comfortable with calculus concepts and how to apply them to solve problems.
• Take mock tests: Taking mock tests can help you identify your strengths and weaknesses and give you practice in solving JEE Advanced-level problems. Use these tests to identify areas to improve and refine your problem-solving approach.
• Focus on understanding: Don't just memorize formulas and equations. Ensure you understand their concepts and how to apply them to solve problems. This will help you in the long run and make it easier to apply the concepts to new and unfamiliar situations.
• Use visual aids: Analytical geometry problems often involve visualizing geometric shapes and relationships. Use diagrams, graphs, and other visual aids to help you understand the problem and visualize the solution.
• Solve previous year's question papers: Solve as many previous year's questions as possible to get a good idea of the questions asked in the exam. This will help you become familiar with the format and difficulty level of the questions and give you practice in solving problems under timed conditions.
• Take breaks: Studying for JEE Advanced can be stressful and exhausting. Take regular intervals to rest and recharge. This will help you stay focused and motivated and prevent burnout.
• Seek help: Don't be afraid to seek help if you struggle with a concept or problem. Talk to your teachers, tutors, or peers for guidance and support. Many online resources are available, such as video tutorials and forums, where you can get help and advice.

Remember, analytical geometry is just one part of the JEE Advanced syllabus. 

Ensure you are also preparing well for the other subjects, and have a good study plan to ensure that you cover all the topics before the exam.

You should also practice solving problems regularly and develop a clear understanding of the concepts. Good luck with your JEE Advanced preparation!