1. MATH-002
Dr. Farhana Shaheen
CONIC SECTION

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. 2
EQUATION OF PARABOLA y 4 px
 Axis of Parabola:
x-axis
 Vertex: V(0,0)
 Focus: F(p,0)
 Directrix: x=-p

8. 2
DRAW THE PARABOLA y 6x
2
y 4 px

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