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10Class 11 Maths

Conic Sections formulas

Standard equations and key properties of the circle, parabola, ellipse and hyperbola for Conic Sections. Comparing the given equation with the standard form is the first step.

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All Maths formulas

Circle

Equation
(x−h)2+(y−k)2=r2\displaystyle (x - h)^2 + (y - k)^2 = r^2
General form
x2+y2+2gx+2fy+c=0\displaystyle x^2 + y^2 + 2gx + 2fy + c = 0

Centre (−g, −f), radius √(g² + f² − c).

Parabola

Standard form
y2=4ax\displaystyle y^2 = 4ax

Focus (a, 0), directrix x = −a.

Latus rectum
4a\displaystyle 4a

Ellipse

Standard form
x2a2+y2b2=1,a>b\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b
Focal distance
c2=a2−b2\displaystyle c^2 = a^2 - b^2
Eccentricity
e=ca<1\displaystyle e = \frac{c}{a} < 1
Latus rectum
2b2a\displaystyle \frac{2b^2}{a}

Hyperbola

Standard form
x2a2−y2b2=1\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
Focal distance
c2=a2+b2\displaystyle c^2 = a^2 + b^2
Eccentricity
e=ca>1\displaystyle e = \frac{c}{a} > 1
Latus rectum
2b2a\displaystyle \frac{2b^2}{a}

Where students slip up

  • Mixing the relations. It's c² = a² − b² for an ellipse, but c² = a² + b² for a hyperbola.
  • Assuming a is always under x². In an ellipse, the larger denominator sets the major axis, and it might be under y².

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