Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

S - 14- 60

PARABOLA

(
i

a:

'

�
�
V
...
�ir��tri

a
a


...


Focal Chord:
A line through the focus of the parabola and touches the parabola at two differe-points is called focal chord
...


Latus Rectum: A line through the focus of the parabola and always perpendicular to the axis o
parabola
...
·

x

a es of vertex V(O,O)

'

Directrix

4a

=

a

x,a=

a

x

2015

S - 15 - 61
,ength of latus rectum=4 !al
"a" taken positive when focus on the
right of origin and negative when focus is on the left of the origin
...


Directrix

PARABOLA WITH AXIS PARALLEL TO X-AXIS AND VERTEX NOT AT ORIGIN
Directrix

x
-

ation of parabol (y-k)2=4a(x-h)
rdinates of focu S(h+a,k)
_e
h of la us rectum=4
...


PARABOLA WITH AXIS PARALLEL TO Y-AXIS ·AND VERTEX

OT A ORIG!

y

a

k a

Directrix

k-a

x
h

Equation of parabola (x-h)2=4a(y-k)
Coordinates of vertex V(h,k)
Coordinates of focus S(h,k+a)
Equation of directrix y+a-k=O
Length of latus rectum=4 [a]
Axis of parabola x-h=O

ELLIPSE
Axis of ellipse => Major Axis

/

VERTICES

CENTRE

MAJOR AXIS

B

MINOR AXIS
END POINTS OF MINOR AXIS

FOCI

2 �-

c

A'

A

a
a-

Distance between centre and vertex OR semi Major Axis

2a-

Distance between Vertices

OR length of Major Axis
B

b-

Semi Minor Axis

2b-

Length of Minor Axis


...
=


...

si-----�-11
C

I

B

A'

a>c

a>b

a= - c2 > 0

a= - c2

= bj

ECCENTRICITY :

c

e=a

---

Condition for ellipse

(e)

c
2b

A

A


...
-ordinates of Vertices A(a,O), A1(-a,O)

Co-ordinates of foci S(c,O), S1(-c,O)
Equation of ellipse

x2

v2

a2 + b2 =

End points of Minor Axis

1

B (O,b), 81(0, -b)

Distance between Diretrices

Equation of Directrices

= 2(!)

CENTRE AT ORIGIN AND AXIS ON Y-AXIS

y

Co-ordinates of centre C(O,O)

D rectrix

A(O,a) , A' (0, -a)

C -ordinates of Vertices
j

Co-ordinates of foci S(O, c), S1(0, -c)
Co-ordinates of end points of minor
B(b,O) ancl 81(-b, 0)
axis
Equation of Directrices

a
Y=+-e

E [ua ion of ellipse � + � = 1

a

ale

B'

c

s·

x

a

x =+-e

S - 14 - 66

CENTRE AT (h,k) AND AXIS PARALLEL TO X-AXIS

y
Dir ctrix

Dir ctrix
ale

B:

k+b
B

k

�
I


...


- ,, --'-1 IVV�

CENTRE AT (h, k) AND AXIS PARALLEL TO Y-AXIS

y
Directrix

a

al

'r-ale

k

a
k

'A'
Directrix
0 -------'h�+-"b"--

_
...
(h, k±a )

End points of Minor Axis (h±b, k)

Equation of Axis x-h=O

Equation of Directrices y=k± ale

Equation of ellipse

(y - k)2

az

+

(x - h)2 - 1
bz

S- 15 - 67

2015

HYPERBOLA
CENTRE

...



...



...
·······

1,/

AXIS OF HYPERBOLA
OR
TRANSVERSE AXIS OF HYPERBOLA

...

:;
...
::-r

CONJUGATE AXIS

A:
...
,

I
I

I�
I

I
I

s

I
I

I
I
I

I

:
...
,

2a

111:

Distance between centre and vertex a (semi transverse axis)
2a
Length of transverse axis
c

Distance between centre and focus

b-

semi conjugate axis

2b

length of conjugate axis

2c

Distance between foci

b

-------=:
...
;AXIS

jv
c

x

S-15 - 69

2015

·--'r'PERBOLA WITH CENTRE AT ORIGIN AND TANSVERSE AXIS ON Y-AXIS
y

c

x

HYPERBOLA WITH CENTRE NOT AT ORIGIN AND TANSVERSE AXIS PARALLEL TO X-AXIS

y

c

0

x

HYPERBOLA WITH CENTRE NOT AT ORIGIN AND TANSVERSE AXIS PARALLEL TO Y-AXIS

y

c

0

x

HYPERBOLA WITH CENTRE NOT AT ORIGIN AND TANSVERSE AXIS ON SOME LINE

y

0

x

S-14-70

CENTRE AT ORIGIN AND TRANSVERSE AXIS ON X-AXIS

y

Co-ordinates of vertices A(a,O), A1(-a, 0)
Co-ordinates of foci S(c,0), 81(-c ,0)
Equation of Directrics

Equation of Hyperbola

a
x=+-e
x2

v2

a2 - b2 =

1

2b2
Length of !atus rectum=a

c
CENTRE AT ORIGIN AND TRANSVERSE AXIS ON Y-AXIS
Co-ordinates of Vertices A(O,a), A1(0, -a)
Co-ordinates of foci S(O,c), 81(0 ,-c)
Equation of Directrics y = ±

Equation of Hyperbola

!

v2

Dire�tr x

x2

a7 - b2

= 1

2b2
Length of latus rectum=a

CENTRE AT (h, k) AND TRANSVERSE AXIS PARALLEL TO X-AXIS
...


I

I

a »,


...


Co-ordinJes of vertices

(hh±

a, k)

Equation of transverse Axis y - k = 0
Equation of Hyperbola

2b2
Length of latus rectum=a

(x - h)2
a2

Co-ordinates of foci (h ± c, k)
Equation of Directrices x = h ±

(y - k)2 - 1
b2

!



---

Title: Parabola,Hyperbola,Ellipse formulas with graphical representation
Description: Following pdf file consists of the information relating curves such as hyperbola,parabola and ellipse. All the formulas are provided under three corresponding headings. What make my notes special is the graphical representation of each and every topic.The notes can provide complete knowledge of these curves to the beginners while they can prove as a great reference to experts

Buy These NotesPreview