Most students over the years have found it difficult to crack JEE Mathematics. However we at Toppr believe that this isn’t entirely true with numerous sections having questions which can be solved using visualization, an inherent skill which ALL students can develop. This article aims at giving you the inside edge that will help you improve your efficiency and waltz your way to success in coordinate geometry which is an evergreen favourite of the paper setters for more than a decade now.
IN COORDINATE GEOMETRY, ALWAYS DRAW DIAGRAMS
This is the first golden rule of coordinate geometry. Make sure that all the given information is translated into a diagram. Try making it accurate as possible since knowing the quadrants and points (explained next) make it easier to find and eliminate answers. Mark whatever is required to solve this problem, in your diagram.
USE STANDARD CONICS TO ELIMINATE
Coordinate geometry questions that show up in the multiple question section can be shortened by eliminating options. Using the position of a point relative to a line, circle or another standard conic can go a long way in providing insights on which options are correct. CAUTION: DO NOT use this in integer answer type or subjective questions where finding this is a waste of time. Be careful with the signs else the entire exercise is pointless.
MUG LESS, VISUALISE MORE
Most of the JEE preparation books are filled with loads of formulae and shortcuts to memorize. We don’t believe in doing so. There are no doubt some important formulae which should be memorised, but the lesser you stress your brain for such material the more you can utilize it to think from first principles. Some of the first principles that you must be familiar with are the focus-directrix property for each conic, the concept of tangent and normal and their inter-relation, director circle etc. Many questions can be reduced to locus of point calculations by applying these relations directly. It is needless to say the lesser you stress on memory the faster you work and better your analytical skill.
PLAY WITH PARAMETERS
Of the various ways available to represent points on a conic, the parametric form is the easiest. Many times choices can easily be identified with the parametric form. Moreover, manipulating calculations is easier since most of the parameters are simply trigonometric values (except parabola). Know all the parametric forms of all the curves and learn to manipulate them to minimize calculation.
LINKED BY COMPREHENSIONS
JEE paper setters love to give coordinate in linked comprehensions. Be it complex situations involving multiple conics or a combination of triangle and circles, there are always challenging paragraphs JEE can cook & serve. Now, in cases of linked comprehensions, more often than not, the later questions in the paragraph give hints to the solutions or approach to take for the first questions. The paper setters want to probe a particular approach through the paragraph and the questions are merely the checkpoints that come along the way. Make sure you read the entire paragraph, sense the approach and think accordingly.
FIND THE CONIC FIRST
In many cases, students might get confused regarding the type of conic especially when questions are in the 2nd degree general form. To eliminate confusion make sure that you apply the discriminant condition using the coefficient values to identify the conic type. Knowing this will help eliminate options and give you the required confidence to put pen on paper during the final moment of bubbling the answer.
SET YOUR AXES THE WAY YOU WANT TO
Most questions do not necessarily specify usage of coordinate systems or involve transformation. In such situations, it is imperative that you transform or choose axes that help in cutting down the calculation time. The last thing you want to do is spend precious minutes on finding large squares and mind boggling square roots. When doing this, make sure you note down relevant changes made in the coordinate systems to avoid the tension building confusion that may ensue.
With this, we would like to point out that all of these techniques in coordinate geometry can be mastered and perfected only with practice over time irrespective of format. Practicing in examination environment while giving tests will help building the confidence needed to deal with the stress that D-Day will throw at you.
Cheers and Good Luck.