Analytical Geometry for JEE Advanced Preparation: Check important tips to prepare

Read the article below to check important tips for effective preparation of Analytical Geometry from JEE Advanced point of view.

Analytical geometry is one of the easiest topics for JEE Advanced though it has a huge weightage. It requires lots of mugging, you need to memorise various formulas and properties. So let's start with coordinate geometry.

Topics in Analytical Geometry

• First of all, your basics of coordinate geometry should be clear, which naturally gets better while preparing for JEE Main. Still, if you have some doubts, you can go through all the problems given in NCERT.

• The very first topic you'll be starting with is Straight Lines. Problems of straight lines are straightforward and it doesn't require much effort. Then comes the family or pair of straight lines. It is more important from JEE Advanced point of view. In JEE Advanced, they generally ask questions that require concepts of various topics, so if they want to ask the question in straight lines, they prefer this topic. Lines through the point of intersection of two given lines, the equation of the bisector of the angle between two lines, concurrency of lines, centroid, orthocentre, in centre and circumcentre of a triangle are some of the important topics which are usually asked. Basically, straight lines are the topic that builds up your concepts for further topics. You should learn and memorise their properties. You should also know how to use the parametric form of the line.

• Next comes the Circle. It is the most important topic of the entire coordinate geometry because the properties and formulas derived will be used throughout. If you want to solve advanced problems, you should know every derivation related to circles. Generally, in JEE Advanced, the questions are asked with the involvement of straight lines in it, for example, an intersection of a circle with a straight line, the equation of a circle through the points of intersection of a circle and a straight line. As I said before, they basically test your combined knowledge of various topics. Generally what they do is, give a multiple-choice question and ask four different things on completely different concepts. Now, here they check your level of preparation. If you don’t know any of the options, you cannot attempt the question. So, it’s better to go through all the topics. Here also parametric form is important as it sometimes makes the problem a lot easier. Finding radical axis, radical centre, an equation of common tangent are some of the important topics from circles that are important from JEE Advanced point of view.
• Next comes the major part of coordinate geometry, which is the Conic Section. The conic section involves the parabola, ellipse and hyperbola. There is a variety of questions that they can make from these topics, involving circle and line in it. Generally, the main properties and theorem used are derived from the properties of a circle. Among these three, you should know all the properties of a parabola. Parabola makes things a little easier because once you become perfect in solving the problems of the parabola, you will not face any problems in solving problems of the other two conics. Questions on finding foci, directrices and eccentricity, parametric equations, equations of tangent and normal should be understood properly. Generally, people forget their general form or sometimes get confused. You can derive them if necessary, but remember, you are preparing for JEE Advanced. During the exam, each second has its own value. Make sure you don't get bewildered. Finding locus is one of the usual questions that is asked in JEE Advanced so have a look through the questions related to it.
• Talking about 3-D geometry you'll not see a wide variety of questions asked in the exam from this topic. Preparing for it is really fun, most of the questions are linked and are given as a puzzle to you. For preparing 3-D geometry first, you should go through NCERT. This will make your basic concepts clear. To prepare for JEE Advanced, you need to learn some new topics such as the equation of a sphere, problems related to four non-coplanar points. There are various types of questions that follow a particular algorithm, so you need to analyze them while solving. It will help you further. Also, there are some derived results that you need to remember as they will save your time during the exam. Study material from your coaching institute is enough for preparation. If you are not going to any coaching, then any Arihant publication book will be good.

Tips for getting a better command on Analytical Geometry

Sometimes, what happens is, due to overconfidence, most of the people stop practising problems. Actually, in coordinate geometry, all the topics are related to each other. When this part of the course gets started, everyone follows the class, but slowly when they reach up to hyperbola, they usually get confident as they do the similar type of questions. This is where the problem begins. This topic requires lots of patience, you may be able to solve questions of parabola but you'll not be able the solve the questions of hyperbola even if it has the same logic involved.

If you want to become a master in any subject, first you need to get familiar with all the topics related to it. It should strike your mind just by seeing the question that this might be the concept involved. Speed is also one important factor that affects your overall performance. For becoming perfect in all this, there is a simple secret, which is practising as much as you can.

Also, you should make short notes or some formulae sheet where you should write all the basic formulae and properties. It really helps to summarize all the formulae on one sheet as you can easily relate them to each other and also your understanding of them also gets better.

Most of you must have joined some coaching institute. So for practising problems, first you should solve the study material of your coaching institute because those are made systematically. Parallelly, you can solve books like S.L. Looney, S.K Goyal, TMH. These books will basically expose you to different types of questions.

Last year papers are also very helpful, not only for mathematics but for all subjects. It is essential that you first try those questions on your own and also put maximum effort to solve them. Those questions basically define the level of JEE. Preferably, you can buy a book of previous years’ papers. It really helps a lot.

Summing up, I would say believe in yourself, put in all your efforts in JEE, work hard and stay focused. You will definitely succeed.

About the Author:

Aman Goel is a co-founder at a Tech Start-up. He holds a BTech in Computer Science Engineering from IIT Bombay with a JEE Advanced AIR 33 (Year 2013).

During his free time, he enjoys writing articles/blogs. He is an Entrepreneur, Coder, Speed-cuber, gamer, and fan of Air crash investigation!

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