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JEE Conic Sections: Parabola, Ellipse, and Hyperbola

JEE Conic Sections: Parabola, Ellipse, and Hyperbola

JEE Conic Sections is one of the most crucial topics in the JEE mathematics. On an average, nearly 5 to 6 questions are asked from this topic in JEE Advanced. Definitely, there will be a paragraph type question (consisting of 2 or 3 questions) from this topic in JEE Advanced. In JEE Main, there will be at least 3 problems (one from each conic). Thus, a high score in this topic can boost up your overall marks and rank. However, JEE conic sections require a good amount of preparation and patience. A huge number of formulas and derivations are associated with this topic.

Study all topics of JEE conic sections with a good understanding of the diagrams and graphs. This will greatly reduce the effort needed to solve any problem on the conics. This is so because having a clear picture of the problem statement is always helpful. Determining your approach is as crucial as the process of actually studying. Keep twisting each question you solve. Make room for new possibilities and it will help you to understand the subject more deeply. Good command over this section provides you a great advantage. It would also help you in solving some tough problems of other chapters (Area under the curve, Application of derivatives etc) graphically.

JEE Conic Sections: Important Books

For most topics of JEE conic sections, it is sufficient to study NCERT textbook to gain a simplified idea about the topic. However, for the level of questions asked in the JEE Main and JEE Advanced, NCERT is not sufficient. You should study from the JEE Main and JEE Advanced specific books. Studying from the Arihant’s Coordinate Geometry book (by S.K. Goyal) is highly recommended. To master the JEE conic sections, you need to have a thorough understanding of the theory and derivations.

JEE Conic Sections: Some important points

  • Learn about every constant and parameter in a conic section, things like vertex, center, focal point, eccentricity, directrix, Latus Rectum, Director Circle etc. Most of these parameters are general and recurring. Some, however, are specific to the type of conic section, eg. major and minor axes (Ellipse), transverse and conjugate axis (Hyperbola), asymptotes (an important property of Hyperbola).
  • JEE conic sections are best prepared in the order Parabola, Ellipse, and Hyperbola. Focus on questions based on tangent, normal, and chord of contact. Please keep in mind, JEE gives a lot of attention to parametric form while framing questions from this topic.
  • A standard-form equation, in turn, can tell you the core information about the conic section itself, ie. the vertex (for parabola) or center (for Ellipse and Hyperbola), the focus, the directrix, the length of latus rectum etc. So try to reduce the given conic equation in standard form. With sufficient knowledge on the definition, parameters, standard equations and a bit of critical thinking, you can quickly solve any type of problem of JEE conic sections with little memorization involved.
  • Questions from Hyperbola, Parabola and Ellipse come with multiple applications like the intersection of curves, finding a bounded area, and common tangents. If you skip these chapters you will face a lot of problems in other important chapters like Area under curve and Application of derivatives.

JEE Conic Sections: Some basic tips

  • A definition is just a rule that governs the shape of the JEE conic sections (whether Ellipse, Hyperbola or Parabola). At first, making a rough diagram of curves may help in visualizing. After considerable practice, you would then be able to perform it all in the head. Anyone who has experience of extremely basic algebra and geometry can readily grasp the idea.
  • Whenever you are not getting any idea what to do, just write down the basic equation of a conic and start plugging in known parameters. You’ll probably get to a point where you’ll have one unknown parameter left. You can use your ordered pair to solve for that parameter.
  • To quickly solve problems of JEE conic section, a possible technique may come from knowing that conic sections share a lot of common characteristics with each other. Finding patterns among these characteristics will help you analyze and solve a diversity of problems.
  • Most of the problem in JEE would deal with Standard Form of conic. So you are advised to focus mostly on it.
  • Problems of conics take a lot of time. So, keep a check on time you spent.
  • There are a lot of similar formula and relations in JEE conic section which might confuse you. To avoid this, write everything on a chart in a comparative manner, and revise it regularly.

JEE Conic Sections: Some Interesting Facts

  • The parabola has an important reflection property. Any ray or line that originates at the focus and strikes the parabola is reflected parallel to the axis of symmetry. Or any line parallel to the axis of symmetry on reflection passes through focus. An important property questions are asked frequently on this concept.
  • Asymptotes are the lines which, as they extend to infinity with the curve, approach nearer and nearer the curve but never actually touch it. The asymptotes of a hyperbola lie on the points of intersection of a circle containing the foci and tangents from the vertices. Pay special attention to asymptotes, you will most probably get questions on them in the JEE.
  • Perimeter of Ellipse : A  useful simple approximation for calculating the perimeter of an ellipse, that is within about 5% of the true value (if  a is not more than 3 times longer than b), is as follows:

    Remember, this is only an approximation to simplify things!!! Mug up this formula, no one knows when JEE puts this approximation in paragraph type questions.

With these points in mind, you can score higher in the JEE conic sections. Prepare accordingly and do your best. Good luck!

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