Mastering Conic Sections: A Comprehensive Guide

Jan 01, 2025

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Dive into the world of conic sections with this detailed guide covering parabolas, circles, ellipses, hyperbolas, and lines. Learn the properties, equations, and applications of each type of conic section.

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Mastering Conic Sections: A Comprehensive Guide

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Parabola, Circle Ellipse, Hyperbola or Line
Ellipse!!!
Parabola, Circle Ellipse, Hyperbola or Line
Ellipse!!!
Parabola, Circle Ellipse, Hyperbola or Line
Parabola!!!
Parabola, Circle Ellipse, Hyperbola or Line
Hyperbola!!!
Parabola, Circle Ellipse, Hyperbola or Line
Circle!!!
Parabola, Circle Ellipse, Hyperbola or Line
Hyperbola!!!
Parabola, Circle Ellipse, Hyperbola or Line
Parabola!!!
Parabola, Circle Ellipse, Hyperbola or Line
Ellipse!!!

Hyperbola

554 views • 9 slides

Hyperbola

Hyperbola. Directrix. e>1 O : center F1, F2 : foci V1, V2 : vertices PF2 – PF1 = V1F2 – V1F1 = V1V2 = 2a Product of shortest distances from P to the asymptotes is a constant. When the asymptotes are perpendicular it is a called a rectangular hyperbola. P. Axis. b. F2. V2. V1.

945 views • 13 slides

Conic Sections Parabola Ellipse Hyperbola

Conic Sections Parabola Ellipse Hyperbola. ZAHIDA DEPARTMENT OF MATHEMATICS UNIVERSITY OF HAIL. Conic Sections. Contents. General Equation of a Conic Section Second Degree Equation Parabola: Definition-- Algebraic and Geometric Examples Ellipse

872 views • 18 slides

Hyperbola and Parabola Review

Hyperbola and Parabola Review. 1.). 4.). 7 .). Since we know the graph opens left and right the term with x 2 is first. 8 .). Since the x is squared and the p is positive, the graph opens up. That means the focus is 3 units to the up and the directrix is 3 units down.

251 views • 7 slides

CONIC SECTIONS ELLIPSE , PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE

OBSERVE ILLUSTRATIONS GIVEN BELOW. CONIC SECTIONS ELLIPSE , PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE THESE CURVES APPEAR ON THE SURFACE OF A CONE WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES. Ellipse. Section Plane Through Generators. Section Plane

622 views • 8 slides

Hyperbola

Hyperbola. By: Leonardo Ramirez Pre Calculus Per.6 Mr. Caballero. Hyperbola. What is a Hyperbola?. The term hyperbola was introduced by the Greek mathematician Apollonius of Perga as well as the terms Parabola, and Ellipse.

710 views • 9 slides

HYPERBOLA

HYPERBOLA. PARTS OF A HYPERBOLA. The dashed lines are asymptotes for the graphs. conjugate axis. vertices. vertices. transverse axis. center. Focus 1. Focus 2.

475 views • 13 slides

10.2 The circle and the ellipse

10.2 The circle and the ellipse. Matt Kwak. Circle. Set of all points in a plane that are at a fixed distance from a fixed point(center) in the plane. With the center ( a, b ) and radius r, standard equation of a circle is (x-a) 2 + (y-b) 2 = r 2. Example .

237 views • 12 slides

Ellipse

Ellipse. Hyperbola. Parabola. Ruđer Josip Bošković. “When I see faded monuments, erased letters which they bore, I think of what will happen with what I am doing!”. Optics. Became a professor of mathematics in Rome. Dubrovnik, hometown. Astronomy. One crater is named after Ruđer Bošković.

474 views • 18 slides

Design of Line, Circle & Ellipse Algorithms

Design of Line, Circle & Ellipse Algorithms. Slope-Intercept Formula For A Line Given a third point on the line: P = (x,y) Slope = (y - y 1 )/(x - x 1 ) = (y 2 - y 1 )/(x 2 - x 1 ) Solving For y y = [(y 2 -y 1 )/(x 2 -x 1 )]x + [-(y 2 -y 1 )/(x 2 -x 1 )]x 1 + y 1

954 views • 21 slides

ellipse

ellipse. Ellipse. The set of all co-planar points whose sum of the distances from two fixed points (foci) are constant. Ellipse. Definition of major and minor axis. minor axis. major axis. Ellipse. major axis. minor axis. Ellipse. Definition of vertices and co-vertices. co-verticies.

441 views • 18 slides

hyperbola

hyperbola. Last Updated: March 11, 2008. Hyperbola. The set of all co-planar points whose difference of the distances from two fixed points (foci) are constant. foci. foci. Hyperbola. Center: (h, k). conjugate axis. vertex. vertex. transverse axis.

1.37k views • 33 slides

Ellipse

Ellipse. Conic Sections. The plane can intersect one nappe of the cone at an angle to the axis resulting in an ellipse. Ellipse. Ellipse - Definition. An ellipse is the set of all points in a plane such that the sum of the distances from two points (foci) is a constant.

1.23k views • 31 slides

ELLIPSE

ELLIPSE. CONSTRUCTION AND ORIGIN. Cross section of a cone. Always as long as the portion of the cone is wide. It is always at an angle All the points lie in the cone End points of ellipse are the edge of a cone. DEGENERATE CASE. “the simple case”

394 views • 10 slides

Hyperbola

Hyperbola. Conic Sections. The plane can intersect two nappes of the cone resulting in a hyperbola. Hyperbola. Hyperbola - Definition. A hyperbola is the set of all points in a plane such that the difference in the distances from two points (foci) is constant.

827 views • 33 slides

hyperbola

hyperbola. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: March 11, 2008. Hyperbola. The set of all co-planar points whose difference of the distances from two fixed points (foci) are constant. foci. foci. Hyperbola. Center: (h, k). conjugate axis.

702 views • 21 slides

hyperbola

hyperbola. Jeff Bivin -- LZHS. hyperbola applet. Graph : Graph and locate the foci. Text Example. Solution . We see that h = 2 and k = 3. Thus, the center of the hyperbola, ( h , k ), is ( 2, 3). 8. 7. 6. 5.

3.51k views • 42 slides

Circle Ellipse

Conic Sections. See video!. Circle Ellipse. Parabola Hyperbola. Circle. Standard Equation of a Circle:. P ( x, y ). (with radius of r and center at ( h,k ):. 2. 2. 2. (. –. ). + (. –. ). =. > 0. x. h. y. k. r. r. C ( h, k ).

271 views • 9 slides

Design of Line, Circle & Ellipse Algorithms

Design of Line, Circle & Ellipse Algorithms. Basic Math Review. Cartesian Coordinate System. Slope-Intercept Formula For A Line Given a third point on the line: P = (x,y) Slope = (y - y 1 )/(x - x 1 ) = (y 2 - y 1 )/(x 2 - x 1 ) Solving For y

407 views • 21 slides

Hyperbola

Hyperbola. Definition : A hyperbola is a set of points in the plane such that the difference of the distances from two fixed points, called foci, is constant. (A hyperbola consist of 2 branches and asymptotes). Vocabulary. Foci: Two fixed points on the transverse axis

362 views • 6 slides

Hyperbola

Hyperbola. Warm Up: Try to recall the standard form of a hyperbola’s equation And use it to find the equation of a hyperbola with a center of (1, -1), a vertex of (3, -1) and a foci at (4, -1). Objective: Be able to get the equation of a hyperbola from given information or the graph

345 views • 8 slides

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Mastering Conic Sections: A Comprehensive Guide

Mastering Conic Sections: A Comprehensive Guide

Presentation Transcript

Hyperbola

Hyperbola

Conic Sections Parabola Ellipse Hyperbola

Hyperbola and Parabola Review

CONIC SECTIONS ELLIPSE , PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE

Hyperbola

HYPERBOLA

10.2 The circle and the ellipse

Ellipse

Design of Line, Circle &amp; Ellipse Algorithms

ellipse

hyperbola

Ellipse

ELLIPSE

Hyperbola

hyperbola

hyperbola

Circle Ellipse

Design of Line, Circle &amp; Ellipse Algorithms

Hyperbola

Hyperbola

Design of Line, Circle & Ellipse Algorithms

Design of Line, Circle & Ellipse Algorithms