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- 1. MATH-002Dr. Farhana ShaheenCONIC 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 WHOSEDISTANCE FROM A FIXED POINT IS EQUAL TOTHE DISTANCE FROM A FIXED LINE. THE FIXEDPOINT IS CALLED FOCUS AND THE FIXED LINE ISCALLED A DIRECTRIX.P(x,y)
- 7. 2EQUATION OF PARABOLA y 4 px Axis of Parabola: x-axis Vertex: V(0,0) Focus: F(p,0) Directrix: x=-p
- 8. 2DRAW 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 OFDISTANCE FROM TWO FIXED POINTS ISCONSTANT. THE TWO FIXED POINTS ARE CALLEDFOCI.
- 14. ELLIPSE a>b Major axis: Minor axis: Foci: Vertices: Center: Length of major axis: Length of minor axis: Relation between a, b, c
- 15. EQUATION OF THE GIVEN ELLIPSE?
- 16. EQUATION OF THE GIVEN ELLIPSE IS
- 17. EARTH MOVES AROUND THE SUN ELLIPTICALLY
- 18. DRAW THE ELLIPSE WITH CENTER AT(H,K)
- 19. ECCENTRICITY
- 20. 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.
- 21. 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.
- 22. HYPERBOLA
- 23. HYPERBOLA Transverse axis: Conjugate axis: Foci: Vertices: Center: Relation between a, b, c
- 24. HYPERBOLA WITH VERTICAL TRANSVERSE AXIS
- 25. ECCENTRICITY E = C/A e = c/a e= 1 Parabola e=0 Circle e>1 Hyperbola e<1 Ellipse
- 26. ECCENTRICITY EELLIPSE (E=1/2), PARABOLA (E=1) ANDHYPERBOLA (E=2) WITH FIXED FOCUS F ANDDIRECTRIX
- 27. HYPERBOLA
- 28. THANK YOU

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