Conic section ppt
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![Page 1: Conic section ppt](https://reader035.fdocuments.us/reader035/viewer/2022081414/5558a9c9d8b42aa6708b53cd/html5/thumbnails/1.jpg)
CONIC SECTION
MATH-002Dr. Farhana Shaheen
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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.
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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
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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.
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PARABOLA
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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)
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EQUATION OF PARABOLA
Axis of Parabola: x-axis Vertex: V(0,0) Focus: F(p,0) Directrix: x=-p
pxy 42
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DRAW THE PARABOLA xy 62
pxy 42
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PARABOLAS WITH DIFFERENT VALUES OF P
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EQUATION OF THE GIVEN PARABOLA?
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PARABOLAS IN NATURE
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PARABOLAS IN LIFE
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ELLIPSE: LOCUS OF ALL POINTS WHOSE SUM OF DISTANCE FROM TWO FIXED POINTS IS CONSTANT. THE TWO FIXED POINTS ARE CALLED FOCI.
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ELLIPSE
a > b Major axis: Minor axis: Foci: Vertices: Center: Length of major axis: Length of minor axis: Relation between a, b, c
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EQUATION OF THE GIVEN ELLIPSE?
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EQUATION OF THE GIVEN ELLIPSE IS
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EARTH MOVES AROUND THE SUN ELLIPTICALLY
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DRAW THE ELLIPSE WITH CENTER AT(H,K)
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ECCENTRICITY
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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.
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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.
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HYPERBOLA
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HYPERBOLA
Transverse axis: Conjugate axis: Foci: Vertices: Center: Relation between a, b, c
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HYPERBOLA WITH VERTICAL TRANSVERSE AXIS
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ECCENTRICITY E = C/A
e = c/a e= 1 Parabola e=0 Circle e>1 Hyperbola e<1 Ellipse
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ECCENTRICITY E ELLIPSE (E=1/2), PARABOLA (E=1) AND HYPERBOLA (E=2) WITH FIXED FOCUS F AND DIRECTRIX
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HYPERBOLA
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THANK YOU