KTUYSBeta
Log inSign up

Cheat sheet · Class 11 · CBSE · Commerce Mathematics

Conic Sections cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

CBSE Class 11 · Mathematics

Cheat sheet

Chapter 10Conic Sections

e = 0 circle, e < 1 ellipse, e = 1 parabola, e > 1 hyperbola.

1. Circle

(x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2

General: x2+y2+2gx+2fy+c=0x^2 + y^2 + 2gx + 2fy + c = 0, centre (−g,−f)(-g, -f), r=g2+f2−cr = \sqrt{g^2 + f^2 - c}.

2. Parabola

EquationFocusDirectrixAxis
y2=4axy^2 = 4ax(a, 0)x = −ax-axis
y2=−4axy^2 = -4ax(−a, 0)x = ax-axis
x2=4ayx^2 = 4ay(0, a)y = −ay-axis
x2=−4ayx^2 = -4ay(0, −a)y = ay-axis

Latus rectum length = 4a.

3. Ellipse & Hyperbola

EllipseHyperbola
Equationx2a2+y2b2=1\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1x2a2−y2b2=1\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1
Relationc2=a2−b2c^2 = a^2 - b^2c2=a2+b2c^2 = a^2 + b^2
Eccentricitye=ca<1e = \dfrac ca < 1e=ca>1e = \dfrac ca > 1
Latus rectum2b2a\dfrac{2b^2}{a}2b2a\dfrac{2b^2}{a}

4. Key Points

  • Conics are sections of a double cone.
  • Foci of ellipse: (±c, 0).
  • Rectangular hyperbola: a = b.
  • Circle is an ellipse with e = 0.

Remember: Circle centre & radius | 4 parabolas | ellipse vs hyperbola

Conic Sections: questions and notes

More Class 11 · CBSE · Commerce Mathematics cheat sheets

Practise Conic Sections

Sign up free to practise the full chapter. Questions you get wrong come back until you've mastered them.

Start practising free

Free to start · No credit card needed