Fabric behind All of Creations

1. CONIC SECTION
MATH-002
Dr. Farhana Shaheen

2. CONIC SECTION
 In mathematics, a conic section (or just
conic) is a curve obtained by intersecting a
cone (more precisely, a right circular conical
surface) with a plane. In analytic geometry, a
conic may be defined as a plane algebraic
curve of degree 2. It can be defined as the
locus of points whose distances are in a fixed
ratio to some point, called a focus, and
some line, called a directrix.

3. CONICS
 The three conic sections that are created
when a double cone is intersected with a
plane.
 1) Parabola
 2) Circle and ellipse
 3) Hyperbola

4. CIRCLES
 A circle is a simple shape of Euclidean
geometry consisting of the set of points in a
plane that are a given distance from a given
point, the centre. The distance between any
of the points and the centre is called the
radius.

5. PARABOLA

6. PARABOLA: LOCUS OF ALL POINTS WHOSE
DISTANCE FROM A FIXED POINT IS EQUAL TO
THE DISTANCE FROM A FIXED LINE. THE FIXED
POINT IS CALLED FOCUS AND THE FIXED LINE IS
CALLED A DIRECTRIX.
P(x,y)

7. EQUATION OF PARABOLA
 Axis of Parabola:
x-axis
 Vertex: V(0,0)
 Focus: F(p,0)
 Directrix: x=-p
pxy 42


8. DRAW THE PARABOLA xy 62

pxy 42


9. PARABOLAS WITH DIFFERENT VALUES OF P

10. EQUATION OF THE GIVEN PARABOLA?

11. PARABOLAS IN NATURE

12. PARABOLAS IN LIFE

13. ELLIPSE: LOCUS OF ALL POINTS WHOSE SUM OF
DISTANCE FROM TWO FIXED POINTS IS
CONSTANT. THE TWO FIXED POINTS ARE CALLED
FOCI.

14. ELLIPSE
 a > b
 Major axis:
 Minor axis:
 Foci:
 Vertices:
 Center:
 Length of major axis:
 Length of minor axis:
 Relation between a, b, c

16. EQUATION OF THE GIVEN ELLIPSE?

17. EQUATION OF THE GIVEN ELLIPSE IS

18. EARTH MOVES AROUND THE SUN ELLIPTICALLY

19. DRAW THE ELLIPSE WITH CENTER AT(H,K)

20. ECCENTRICITY

21. ECCENTRICITY IN CONIC SECTIONS
 Conic sections are exactly those curves that,
for a point F, a line L not containing F and a
non-negative number e, are the locus of
points whose distance to F equals e times
their distance to L. F is called the focus, L the
directrix, and e the eccentricity.

22. CIRCLE AS ELLIPSE
 A circle is a special ellipse in which the two
foci are coincident and the eccentricity is 0.
Circles are conic sections attained when a
right circular cone is intersected by a plane
perpendicular to the axis of the cone.

23. HYPERBOLA

24. HYPERBOLA
 Transverse axis:
 Conjugate axis:
 Foci:
 Vertices:
 Center:
 Relation between a, b, c

25. HYPERBOLA WITH VERTICAL TRANSVERSE AXIS

26. ECCENTRICITY E = C/A
 e = c/a
 e= 1 Parabola
 e=0 Circle
 e>1 Hyperbola
 e<1 Ellipse

27. ECCENTRICITY E
ELLIPSE (E=1/2), PARABOLA (E=1) AND
HYPERBOLA (E=2) WITH FIXED FOCUS F AND
DIRECTRIX

28. HYPERBOLA

30. THANK YOU