Conic Sections

Those who are preparing for any competive exam such as JEE Main, NDA and others really need to memorise formulas. Check the important formulas below;  

Circle

• Standard equation (center at origin): $x^2+y^2=r^2$
  $x^2 + y^2 = r^2$

• General form: $x^2 + y^2 + 2gx + 2fy + c = 0$

• Center = (–g, –f), Radius = ?(g² + f² – c)

 Parabola: 

• Standard form (horizontal axis): $y^2=4ax$
  $y^2 = 4ax$

• Standard form (vertical axis): $x^2=4ay$
  $x^2 = 4ay$

• Vertex: (0, 0)

• Focus: (a, 0) or (0, a)

• Directrix: x = –a or y = –a

• Latus rectum = 4a

Ellipse: Check all the important topics related to this topic below;

• Standard form (major axis along x-axis): 

  • $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ where a > b

  • Eccentricity: $e=\sqrt{1?\frac{b^2}{a^2}}$
    $e = \sqrt{1 - \frac{b^2}{a^2}}$

• Foci: (±ae, 0)

• Latus rectum: $\frac{2b^2}{a}$

$$Hyperbola: Students can check important formulae related to this topic below;

• Standard form (transverse axis along x-axis):
  $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$

• Eccentricity:
  $e = \sqrt{1 + \frac{b^2}{a^2}}$

• Foci: (±ae, 0)

• Latus rectum: $\frac{2b^2}{a}$

• Asymptotes:
  $y=\pm \frac{b}{a}x$

There are various topics discussed in the class 11 Maths Conic Section chapter, read below;

• Definition of Conic Sections

• Circle – Standard and general equations

• Parabola – Focus, directrix, latus rectum, standard forms

• Ellipse – Major/minor axes, foci, eccentricity

• Hyperbola – Transverse/conjugate axes, asymptotes, standard form

• Latus Rectum – For all conics

• Eccentricity – For circle, parabola, ellipse, hyperbola

• General Equation of Conics – Classification using second-degree equations

• Graphical Representation & Examples

Students can use our NCERT Solutions for Conic Sections, to revise these topics and master these topics for board and competitive exams.