College Algebra & Trigonometry, 2018a

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Chapter 5 Conic Sections - Circle and Parabola The conic sections as originally conceived in ancient Greece were “slices” of two cones tip-to-tip. Slicing this figure in different ways produces each of the four conic sections - Circle, Ellipse, Parabola and Hyperbola. This chapter will examine the Circle and the Parabola. 5.1 The Equation of the Circle The equation for a circle is typically given as: (x − h) 2 +(y − k) 2 = r 2 In this equation, the point (h, k) represents the center of the circle and r represents the radius of the circle. This equation is derived from the distance formula. The definition of a circle is the locus (or collection) of points that are equidistant from a given point (the center of the circle). So, taking this definition, we can say that any point (x, y) that is on the circle should be a distance of r from the center. Using the distance formula: d = √ (x 1 − x 2 ) 2 +(y 1 − y 2 ) 2 257
258 CHAPTER 5. CONIC SECTIONS - CIRCLE AND PARABOLA Squaring both sides: d 2 =(x 1 − x 2 ) 2 +(y 1 − y 2 ) 2 In this situation, the distance d is the radius of the circle, r. This distance should be the same for all points on the circle. So any point on the edge of the circle, (x, y) should be a distance of r from the center of the circle, (h, k). (x − h) 2 +(y − k) 2 = r 2
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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88 CHAPTER 2. POLYNOMIAL AND RATION
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College Algebra & Trigonometry, 2018a

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