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Cheat sheet · JEE Preparation 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.

JEE · Mathematics

Cheat sheet

Class 11 · 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

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