Conic section
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This document discusses conic sections, which are curves formed by the intersection of a cone with a plane. The three types of conic sections are circles, ellipses, and hyperbolas. Parabolas are also conic sections. Circles are defined as all points equidistant from a center point. Ellipses are defined as all points whose sum of distances to two focal points is a constant. Hyperbolas are defined as two branches where the difference between the distances to two focal points is a constant. The eccentricity parameter relates the conic section's shape to the distance between its foci and directrix.
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Conic section
- 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?
- 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