Knowledge organisers

Conic Sections: CBSE Class 11 Maths knowledge organiser

Everything to know about conic sections on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Conic section: A curve made by cutting a double cone with a plane: circle, ellipse, parabola or hyperbola.
Focus and directrix: A parabola is the set of points equidistant from a fixed point (focus) and a fixed line (directrix).
Eccentricity: e = c/a, which measures how stretched a conic is.

Key formulas

Circle, centre \((h,k)\)	\((x-h)^2+(y-k)^2=r^2\)
\(x^2+y^2+2gx+2fy+c=0\)	\(\text{centre }(-g,-f),\ r=\sqrt{g^2+f^2-c}\)
Parabola \(y^2=4ax\)	\(\text{focus }(a,0),\ \text{directrix }x=-a,\ \text{LR }4a\)
Ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), \(a>b\)	\(c^2=a^2-b^2,\ e=\tfrac ca<1,\ \text{LR }\tfrac{2b^2}a\)
Hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)	\(c^2=a^2+b^2,\ e=\tfrac ca>1,\ \text{LR }\tfrac{2b^2}a\)

Worked example

Find the centre and radius of \(x^2 + y^2 + 8x - 2y - 8 = 0\).

\((x + 4)^2 + (y - 1)^2 = 25\): centre \((-4, 1)\), radius \(5\).

Common mistakes

\(c^2 = a^2 + b^2\) for an ellipse, or \(c^2 = a^2 - b^2\) for a hyperbola: they are the other way round.
Reading \(a\) from \(4a\): in \(y^2 = 12x\), \(a = 3\), not \(12\).
Placing the foci on the wrong axis: they lie on the axis of the larger denominator (ellipse) or of the positive term (hyperbola).
Radius from the general form without the square root, or with the sign of \(c\) wrong.

You should be able to…

Read centre and radius, and foci, vertices, eccentricity and latus rectum from standard equations.
Write the equation of a circle, parabola, ellipse or hyperbola from given features.
Analyse a conic fully, including chords, tangency to axes and the focus property in applications.
Find a conic from points on it and use the defining distance properties.

The printable sheet

Conic Sections knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Conic Sections knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers