Education

Important Points On Conic Section

In 2022, the JEE Main exam will be conducted in two sessions. According to the latest notification by the NTA, the exam will be held in the months of June and July. As far as the JEE Main exam is concerned, the conic section is a topic of great importance. Students can easily score on this topic if learnt properly. 3 to 4 questions can be expected from this topic for any entrance exam. While learning conic sections, students should understand the topic properly so that they can easily crack conic section problems. 

The three types of the conic sections include hyperbolas, parabolas and ellipses. We get different kinds of conics according to the position of the intersecting plane with respect to the cone and by the angle made by it with the vertical axis of the cone. Let β be the angle made by the intersecting plane with the vertical axis of the cone. When the plane cuts the nappe of the cone, we get the following scenarios. If β = 900, the section will be a circle. If 0 ≤ β < α, the curve of intersection is a hyperbola.  If α <  β < 900, the section is an ellipse. It is a set of all points on a plane whose distance from two points adds up to a constant. The eccentricity will be less than 1. 

Standard Equation

The standard equation is given by (x2/a2) + (y2/b2) = 1, where a>b. Here a is the semi-major axis, and b is the semi-minor axis. The latus rectum is a straight line passing through the foci of the conic and perpendicular to the major axis of it. It is the focal chord, which is parallel to the directrix of the ellipse.

Things to Remember

  • Length of Latus Rectum = (2b2/a)
  • Length of major axis = 2a
  • Length of minor axis = 2b
  • Equation of directrix, x = +a/e
  • Area = πab

Equation of Tangent

The tangent is a line that touches a point on the curve of the ellipses. Let the point (x1, y1) be on the curve. Then slope is given by dy/dx at (x1, y1). The equation of tangent to the curve is given by y-y1 = (-b2x1/a2y1)(x-x1). 

Circle

A circle is the locus of points that moves in a plane in such a way that its distance from a fixed point is always constant. The standard equation of a circle with radius ‘r’ and centre (0, 0) is given by x2 + y2 = r2. In general form, the equation is given by (x-h)2 + (y-k)2 = r2, where (h, k) is the centre and r is the radius. Students are advised to go through the JEE revision notes on circles so that they will be thorough with the formulas and important points from this topic. 

Students are recommended to practice a maximum number of mock tests. This will help them to improve their speed of solving the problems. It will also help them to boost their confidence and reduce exam stress. Logon to BYJU’S for important formulas pdf on conic section and previous years’ JEE solved question papers.

Shehad

Blogger By Passion, Programmer By Love and Marketing Beast By Birth.

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