Co-ordinate your geometry - co-ordinate geometry

Co-ordinate geometry has a huge weightage in JEE and it is considered to be the easiest topic in JEE maths.
First of all, a chapter wise analysis, then relevant books and then concluding remarks are mentioned in this post.

1.) Basics : Cartesian coordinates, distance between two points, section formulae, shift of origin etc. They form the backbone of Co-ordinate 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, angle between two lines, 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 as mentioned in JEE syllabus. Understand the various forms of a line and learn to apply the best form in a particular scenario. 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, 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 a number of formulas such as - length of tangent from a point, equation of chord of contact, equation of chord with a given midpoint, equation of common tangent, finding radical axis, radical centre, 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 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 se 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. Auxiliary circle helps a lot in solving the questions of this chapter. Locus problems are frequently asked from this chapter. 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. 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.

Books : TMH is the best book if you are aiming for a good rank. If you are looking to try something challenging and want to convince yourself that you know coordinate geometry, then go for Arihant Coordinate Geometry by SK Goyal. It's a good book. It contains enough subjective and objective problems. Make sure you do all

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 parameter. These are the most important things and most problems will be done if you do them.

Revision : Any review package might help. Make sure you revise the formulas from some reliable source. Best way is to write down all of them in 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).

Finally : I request you all not to ask me "Is this book enough for JEE ?", "will I get under 1000 rank if I do this ?".
I really don't know the answer to such questions. Nothing is enough for JEE. You can solve all the material available but still, you might not get the expected marks because of poor examination temperament (about which I will write soon in my next post).

All the best.
Enjoy coordinate geometry