fundamentals of algebra 2a chapter 9 powerpoint presentation conic sections
DESCRIPTION
FUNDAMENTALS OF ALGEBRA 2A CHAPTER 9 POWERPOINT PRESENTATION CONIC SECTIONS. CONIC SECTIONS. LEARNING TARGETS. AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: IDENTIFY THE STANDARD FORM OF EQUATIONS FOR CIRCLES,ELLIPSES, PARABOLAS, AND HYPERBOLAS REWRITE EQUATIONS - PowerPoint PPT PresentationTRANSCRIPT
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FUNDAMENTALS OF ALGEBRA 2A CHAPTER 9 POWERPOINT
PRESENTATIONCONIC SECTIONS
CONIC SECTIONS
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LEARNING TARGETS
• AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO:
• IDENTIFY THE STANDARD FORM OF EQUATIONS FOR CIRCLES,ELLIPSES, PARABOLAS, AND HYPERBOLAS
• REWRITE EQUATIONS• DETERMINE: CENTER,RADIUS, FOCUS OR FOCI,
DIRECTRIX, ASYMPTOTES FOR CONIC SECTIONS• IDENTIFY ECCENTRICITY
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THE CIRCLEVOCABULARY
• SECTION – AN INTERSECTION OF A PLANE WITH A THREE-DIMENSIONAL FIGURE
• CONIC SECTION – AN INTERSECTION OF A PLANE WITH A CONE
• CIRCLE – THE SET OF POINTS THAT ARE AT A FIXED DISTANCE CALLED A RADIUS, FROM A FIXED POINT CALLED THE CENTER
• RADIUS – DISTANCE FROM THE CENTER OF A CIRCLE OR SPHERE TO THE EDGE
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CONIC SECTIONS
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OTHER VIEW OF CONIC SECTIONS
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THE CIRCLE
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CONIC SECTION – THE CIRCLE
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Equation for a Circle
• Standard Form: x² + y² = r²• You can determine the equation for a circle
by using the distance formula then applying the standard form equation.
• Or you can use the standard form.• Most of the time we will assume the center is
(0,0). If it is otherwise, it will be stated.• It might look like: (x-h)² + (y – k)² = r²
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ELLIPSES
• ELLIPSE – A SET OF POINTS IN A PLANE SUCH THAT THE SUM OF THE DISTANCE FROM TWO FOCI TO ANY POINT ON THE ELLIPSE IS CONSTANT
• FOCUS (FOCI - plural) – ONE OF TWO FIXED POINTS WITHIN IN AN ELLIPSE SUCH THAT THE SUM OF THE DISTANCES FROM THE POINTS TO ANY OTHER POINT ON THE ELLIPSE IS CONSTANT
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What does it look like?
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Other Ellipses
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One More Ellipse
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Vocabulary for Ellipses
• VERTICES – FOR AN ELLIPSE, THE Y AND X INTERCEPTS ARE THE VERTICES
• MAJOR AXIS – FOR AN ELLIPSE, THE LONGER AXIS OF SYMMETRY, THE AXIS THAT CONTAINS THE FOCI
• MINOR AXIS – FOR AN ELLIPSE, THE SHORTER AXIS OF SYMMETRY
• CENTER – FOR AN ELLIPSE, THE INTERSECTION OF THE MAJOR AND MINOR ARCS
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Equation for an Ellipse
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Parts of an Ellipse
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EXAMPLES
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MORE ABOUT ELLIPSES
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HYPERBOLAS
• HYPOBERLA – A SET OF POINTS SUCH THAT THE DIFFERENCE OF THE DISTANCES FROM TWO FIXED POINTS TO ANY POINT ON THE HYPERBOLA IS CONSTANT
• VERTICES – X OR Y INTERCEPTS OF A HYPERBOLA
• ASYMPTOTE – A STRAIGHT LINE THAT A CURVE APPROACHES BUT NEVER REACHES
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WHAT DOES IT LOOK LIKE?AND WHAT IT ITS FORMULA?
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ASYMPTOTES (IN RED)
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ASYMPTOTES
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PARABOLAS
• PARABOLAS – A SET OF POINTS IN A PLANE THAT ARE EQUIDISTANT FROM A FOCUS AND A FIXED LINE – THE DIRECTRIX
• DIRECTRIX – THE FIXED STRAIGHT LINE THAT TOGETHER WITH THE POINT KNOWN AS THE FOCUS SERVES TO DEFINE A PARABOLA.
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WHAT DOES IT LOOK LIKE?
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ECCENTRICITY
• ECCENTRICITY – A RATIO OF THE DISTANCE FROM THE FOCUS AND THE DISTANCE FROM THE DIRECTRIX.
• EACH SHAPE HAS ITS OWN ECCENTRICY: CIRCLE, PARABOLAS, HYPERBOLAS, AND ELLIPSES.
• Circle: e = 0• Ellipse: e = 0< e < 1• Parabola: e = 1• Hyperbola: e > 1
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WHAT DOES IT LOOK LIKE? FOR A PARABOLA
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FOR AN ELLIPSE
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IN REAL LIFE - ELLIPSES
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IN REAL LIFE - PARABOLAS
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MORE PARABOLAS
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IN REAL LIFE – HYPOBERLAS
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CONIC SECTIONS – WHO KNEW?