Coordinate geometry

Co-ordinate geometry is less about the concept and more about how fast you can see the actual trick to solve the problem.

Co-ordinate geometry has a huge weightage in JEE and it is considered to be the easiest topic in JEE maths. Coordinate geometry questions are widely asked in both jee main and advanced with a huge weightage .

Coordinate geometry is the implementation of the concepts of Euclidean geometry on the co-ordinate system with at least two axes. You might be knowing that, this convention of using two perpendicular axes to represent a point, is known as Cartesian coordinate system.

First of all, a chapter-wise analysis, and then concluding remarks are mentioned in this post.

1.) Basics: Cartesian coordinates, the distance between two points, section formulae, a shift of origin, etc. They form the backbone of Coordinate geometry. Make sure to learn all formulas by heart. Locus problems form another set of problems from the point of JEE. Master them

2.) Straight lines: Equation of a straight line in various forms, the angle between two lines, a distance of a point from a line. Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines, centroid, orthocentre, incentre, and circumcentre of a triangle. These are the topics mentioned in JEE syllabus. Understand the various forms of a line and learn to apply the best form in a particular scenario. The Family of straight lines is most important from the point of view of JEE problems. Also, make sure to learn how and when to apply the parametric form of a straight line.

3.) Circles: Equation of a circle in various forms, equations of tangent, normal, and chord.

Parametric equations of a circle, the intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles, and those of a circle and a straight line.

It’s the simplest chapter. Understand the standard equations. This chapter contains formulas such as – length of the tangent from a point, the equation of chord of contact, equation of chord with a given midpoint, equation of common tangent, finding radical axis, radical center, etc. The formulas derived here are general and apply to ellipse, parabola, and hyperbola as well. So better learn them by heart. The parametric form of a circle is very important.

4.) Parabola: Most of the equations that are derived in the Circles chapter will work here. The parametric form is really important in all chapters of conics. An interesting topic is the reflection property of parabola which you might like to learn for solving paragraph-type questions in JEE. Note that paragraphs are common from the chapters of coordinate geometry so better be prepared to see something new on JEE day. You won’t be given the same old beaten-up problems.

5.) Ellipse: Much of same as Circles. Again the parametric form is important. The Auxiliary circle helps a lot in solving the questions of this chapter. Locus problems are frequently asked from this chapter. The Parametric form will help you in solving locus problems.

6.) Hyperbola: Much of same as Circles and ellipse. Simple but confusing. Conjugate hyperbola and asymptotes and their properties are important. Some people face problems in this chapter. The Reason is that this chapter marks the end of coordinate geometry. So, usually, people get bored till this time and tend to neglect it. But keep in mind that paper setters know all this. And they are ready to trap you. A good student cannot afford to miss any chapter.

TMH for good mcq questions
SL Loneybeginner’s best book
CengageG Tewani
Arihant’s Coordinate
SK Goyal

Concluding Remarks Make sure that you know the parametric form of each curve, equation of tangent of slope “m”, equation of normal of slope “m”, equation of tangent, and normal at any point (x,y) or in terms of a parameter. These are the most important things and most problems will be done if you do them.

 Make sure you revise the formulas from some reliable source. The best way is to write down all of them on a sheet of paper and revise regularly. You will learn them only when you apply them. So solve as many problems as you can. You will enjoy it. For revision, you may try TMH (unsolved problems).

JEE tests your basics. It checks how well you know any concepts. So, be thorough with the concepts. Follow the following steps to prepare well:

Try visualizing the question instead of memorizing or mugging up the answer.

There is a lot of similar formula and relations in Coordinate Geometry which might confuse you. To avoid this, write everything on a chart in a comparative manner.

Problems of Coordinate Geometry take a lot of time. So, keep a check on what you spent

on every question. Try to practice as much as you can to enhance your speed.

Make a note of silly mistakes which you commit while solving questions.

Many students have a myth that problems of Coordinate Geometry are time-consuming. It is but you need to find hints in the information provided and you will definitely find a way out to solve it faster. Good Command over Coordinate Geometry provides an additional advantage to you. So, “TRY AND TRY UNTILL YOU SUCCEED”

Doubts are a part of the learning process and you are bound to come across a few every day. And don’t hesitate to ask for help when you do. You could seek the help of your teacher at school but that might require you to wait until you reach school. Instead, you could have online educational apps like DOUBTBUDDY that help you understand complex problems and concepts. Moreover, the app is well known for its use of clearing students doubts preparing for IITJEE and NEET . You could also get rid of your fear of exams by getting your doubts cleared instantly. Download it now .

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