College Algebra & Trigonometry, 2018a

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5.1. THE EQUATION OF THE CIRCLE 265 17) 2x 2 +2y 2 − 10x − 18y =1 18) 2x 2 +2y 2 − 5x + y =0 19) 9x 2 +9y 2 +9x − 27y +1=0 20) 2x 2 +2y 2 − 7x + y =0
266 CHAPTER 5. CONIC SECTIONS - CIRCLE AND PARABOLA 5.2 The Equation of the Parabola The equation of the parabola is often given in a number of different forms. One of the simplest of these forms is: (x − h) 2 =4p(y − k) A parabola is defined as the locus (or collection) of points equidistant from a given point (the focus) and a given line (the directrix). Another important point is the vertex or turning point of the parabola. If the equation of a parabola is given in standard form then the vertex will be (h, k). The focus will be a distance of p units from the vertex within the curve of the parabola and the directrix will be a distance of p units from the vertex outside the curve of the parabola. This value (p) is called the focal distance. Focus: (h, k + p) Vertex: (h, k) Directrix: y = k − p Any point on the curve of the parabola is equidistant from the focus (h, k + p) and the directrix (h, k − p). Notice that the focus is a point and is identified with the coordinates of the point while the directrix is a line and is identified with the equation for that line.
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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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