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Locus – Equation of Circle Page 5
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Essential Question: What is the difference between a linear equation, quadratic equation, and the equation of a circle? Page 5
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Identify the following equations as linear, quadratic or UNKNOWN: Page 5
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Equation of a Circle (h,k) are the coordinates of the center of the circle r is the radius of the circle Notice that the signs of the center of the circle are opposite of what they are in the equation! Page 5
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More examples:
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and write the equation of each circle. Page 5
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5. The locus of points is a circle centered at the origin with a radius of 6 6. The locus of points is a circle centered at the origin with a radius of 10 Page 5
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Essential Question: What is the difference between a linear equation, quadratic equation, and the equation of a circle? Page 5
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5 Basic Loci
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Find points equidistant from these two fixed points Given: A and B The locus of points is the perpendicular bisector of the segment formed by connecting AB
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Find points equidistant from these two intersecting lines. The locus of points is a pair of lines, which bisect the angles formed by the intersecting lines.
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Find points equidistant from these two parallel lines. The locus of points is a line, parallel to the original lines, midway between them.
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Find points that are at a distance d from the line. The locus of points is a pair of lines parallel to the given line, at a distance d from the line. All points are d distance away
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Find points that are at a distance d from the fixed point A. The locus of points is a circle whose center is point A and the length of whose radius is the distance d. Given:
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Homework Page 5 8,9,10,18,19,23,24,25, 30,31
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