Conic Sections- Circle, Parabola, Ellipse, Hyperbola all topics covered. this is a presentation with excelent animations and explatition.

1. CONIC SECTIONS
XI C

2. α β
THE INTERSECTION OF A PLANE WITH A CONE,
THE SECTION SO OBTAINED IS CALLED A
CONIC SECTION
V
m
Lower
nappe
Upper
nappe
Axis
Generator
l
This is a conic section.

3. TYPES OF CONIC SECTIONS

4. CIRCLE
A CIRCLE IS THE
SET OF ALL
POINTS ON A
PLANE THAT ARE
EQUIDISTANT
FROM A FIXED
POINT ON A
PLANE.
O
P(x,y)

5. (h,k)
C
P(x,y)
O (0,0)
x² + y² = r² (x – h) ² + (y – k) ² = r²
α β
When β = 90°, the section is a circle
Standard Equation General Equation

8. TYPES OF CONIC SECTIONS

9. ELLIPSE
AN ELLIPSE IS THE SET
OF ALL THE POINTS ON A
PLANE,
WHOSE SUM OF
DISTANCES FROM TWO
FIXED TWO REMAINS
CONSTANT.
P
P P
F F
¹
³²
²¹

10. α β
O
(0,c)
(0,-c)
(-b,0) (b,0)
(0,-a)
(0,a)
x² y²
a² b²
— —+ = 1—+
x² y²
b² a²
— = 1
(-c ,0) (c, 0)
When α < β < 90°, the section is an ellipse
Vertical Ellipse
Horizontal Ellipse
(0,-b)
(0,b)
(a,0)(-a,0)

12. .

13. TYPES OF CONIC SECTIONS

14. A PARABOLA IS THE
SET OF ALL POINTS
IN A PLANE THAT
ARE EQUIDISTANT
FROM A FIXED POINT
A
B
V
PARABOLA
(VERTEX)
F
( focus)
1 2 3 4O
P
1
P2

15. α
β
F(a,0)O
x=-a
y² = 4ax
X' X
Y'
Y
F(-a,0) O
x=+a
y² = -4ax
X' X
Y'
Y
F(0,-a)
O
y = a
x² = 4ay
X' X
Y'
Y
F(0,a)
O
y = -a
x² = -4ay
X' X
Y'
Y
When α = β, the section is an parabola
Horizontal Parabola Horizontal Parabola
Vertical Parabola Vertical Parabola

18. TYPES OF CONIC SECTIONS

19. HYPERBOLA
F ( focus)V
(verte
x)
A
B
A HYPERBOLA IS THE
SET OF ALL POINTS,THE
DIFFERENCE OF WHOSE
DISTANCES FROM TWO
FIXED POINTS IS
CONSTANT
V
(verte
x)
F ( focus)

20. α β
Transverse
axis
F
Conjugate axis
F(c ,0)(a ,0)( -c ,0)
(-a ,0)
O
F
F(0 ,c)
(0 ,a)
(0 ,-c)
(0 ,-a)
O
¹
¹
²
²
x² y²
a² b²
— —- = 1
-
y² x²
a² b²
— —- = 1
When 0 ≤ β < α; the plane cuts through both the nappes & the
curves of intersection is a hyperbola

22. HYPERBOLIC PARABOLOIDSUNDIAL
THERMAL POWER PLANT

23. Conic Section Standard Eq. General Eq.
Circle x² + y² = r² (x – h) ² + (y – k) ² = r²
Parabola y² = 4ax (y-k)² = 4a(x+h)
Ellipse
Hyperbola
x² y²
a² b²
— —+ = 1
(x-h)² (y-k)²
a² b²
— + — = 1
x² y²
a² b²
— —- = 1
(x-h)² (y-k)²
a² b²
— - — = 1