Conic Sections PDF

Conic sections Prepared by: Harry G. Quiambao Learning Goal At the end of the lesson, you should be able to illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases. HISTORY The topic of conic sections has been arou...

Conic sections Prepared by: Harry G. Quiambao Learning Goal At the end of the lesson, you should be able to illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases. HISTORY The topic of conic sections has been around for many centuries and actually came from exploring the problem of doubling a cube. Conic section date back to Ancient Greece and was thought to discover by Menaechmus around 360-350 B.C. To solve the case of “doubling the cube” he focused on mean proportions and the use of construction of a cone. Eventually, his solution became known as “Conic sections”. Progress: CONIC SECTIONS A conic section is a curve formed by the intersection of a plane and double right circular cone Progress: CONIC SECTIONS We introduce conic sections (or conics), a type of curve that appears frequently in nature and has applications in other fields. A circle, one of the first shapes we learned, is a conic. The trajectory of a ball when thrown is a parabola. Each planet's orbit around the sun is an ellipse. The properties of hyperbolas have been used in the design of various telescopes and navigation systems. Progress: CONIC SECTIONS The hyperbola, parabola, and ellipse are the three types of conic sections. The circle is a special case of the ellipse, and it is interesting enough in its own right that it was once referred to as a fourth type of conic section. Progress: Illustration of the different types of conic sections CIRCLE When the plane is horizontal Illustration of the different types of conic sections PARABOLA When the plane intersects only one cone to form an unbounded curve Illustration of the different types of conic sections ELLIPSE When the tilted plane intersects only one cone to form a bounded curve Illustration of the different types of conic sections HYPERBOLA When the plane (not necessarily vertical) intersects both cones to form two unbounded curves A plane and the cones can also intersect in other ways, forming what are known as degenerate conics: a point, one line, and two lines. A Point One Line Two Lines ENHANCE a curve formed by the intersection of a plane and Conic Section is ____________________. double right circular cone Circle, ellipse, parabola, and hyperbola are ______________________________. Conic Sections ENRICH Identify the conic sections in architecture. 1. Eiffel Tower _______________ 2. Farmer’s Cottage Deluxe Summer House _________________ 3. Tycho Brahe Planetarium _______________ 4. McDonnell Planetarium _______________ Eiffel Tower Parabola Farmer’s Cottage Deluxe Summer House CIRCLE Tycho Brahe Planetarium ELLIPSE McDonnell Planetarium HYPERBOLA ESTABLISH ACTIVITY No. 1 Think and create! Think about how you'll show all of the conic sections in one figure. A new sheet of paper should be used. APPLICATION OF CONIC SECTIONS