Are these Conic Sections notes free?

Yes. The full 4-page Conic Sections sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Conic Sections revision sheet cover?

Conic sections, and where they come from, Eccentricity: the limiting cases, Circle: centre-radius and general form, centre (h,k), radius r, general form, centre and radius drop out of g,f,c, centre, radius, real only when g^2+f^2-c>0, Worked: centre and radius from the general equation, Parabola, standard forms, opens right, a>0, opens left, a>0, opens up, a>0.

Is this for Class 11 CBSE Mathematics?

It is written from the NCERT syllabus, so it serves CBSE and any board that follows NCERT for Mathematics.

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Conic Sections — Class 11 CBSE Mathematics revision notes

A 4-page visual revision sheet for Conic Sections, written for Class 11 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Conic Sections revision notes, page 1 of 4 — A preview of page 1 — all 4 pages open full size in the app.

Conic Sections in one look

circle, parabola, ellipse, hyperbola, one number apart

Conic sections, and where they come from

each curve is points P obeying one distance rule: a fixed focus, a fixed directrix
eccentricity e=PF/PM, focus distance over directrix distance, is the SINGLE deciding number
e=0: circle. 0<e<1: ellipse. e=1: parabola. e>1: hyperbola, and these four ranges never overlap

Eccentricity: the limiting cases

e=0 — circle, foci merge at the centre
0<e<1 — ellipse, bounded closed curve
e=1 — parabola, one focus, one directrix, one branch
e>1 — hyperbola, two unbounded branches

Circle: centre-radius and general form

centre (h,k), radius r (x-h)^2+(y-k)^2=r^2
general form, centre and radius drop out of g,f,c x^2+y^2+2gx+2fy+c=0
centre (-g,-f)
radius, real only when g^2+f^2-c>0 r=√g^2+f^2-c

Worked: centre and radius from the general equation

Q. find the centre and radius of the circle x^2+y^2-4x+6y-3=0

match against x^2+y^2+2gx+2fy+c=0: 2g=-4 so g=-2, 2f=6 so f=3, c=-3
centre = (-g,-f)=(2,-3)
radius: r=√g^2+f^2-c=√(-2)^2+3^2-(-3)
=√4+9+3=√16=4

Answer: centre (2,-3), radius 4

Page 1 of 4. The full sheet, all 4 pages, opens free in the app.

What this Conic Sections sheet covers

Conic sections, and where they come from
Eccentricity: the limiting cases
Circle: centre-radius and general form
centre (h,k), radius r
general form, centre and radius drop out of g,f,c
centre
radius, real only when g^2+f^2-c>0
Worked: centre and radius from the general equation
Parabola, standard forms
opens right, a>0
opens left, a>0
opens up, a>0
opens down, a>0
Focus, directrix, latus rectum for y²=4ax
The other orientation
Ellipse, standard form (major axis along x)
a>b>0
eccentricity
foci
relation between a, b and e
latus rectum
Sum of focal distances, the defining property
Worked: eccentricity and foci from the equation
Hyperbola, standard form
transverse axis along x
The sign that separates them
Identify the conic from its eccentricity
General second-degree recap
Symbols
Traps that cost marks
Tricks that save time

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