Locus – Equation of Circle Page 5. Essential Question: What is the difference between a linear equation, quadratic equation, and the equation of a circle?

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Presentation transcript:

Locus – Equation of Circle Page 5

Essential Question: What is the difference between a linear equation, quadratic equation, and the equation of a circle? Page 5

Identify the following equations as linear, quadratic or UNKNOWN: Page 5

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

More examples:

Page 5

and write the equation of each circle. Page 5

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

Essential Question: What is the difference between a linear equation, quadratic equation, and the equation of a circle? Page 5

5 Basic Loci

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

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.

Find points equidistant from these two parallel lines. The locus of points is a line, parallel to the original lines, midway between them.

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

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:

Homework Page 5 8,9,10,18,19,23,24,25, 30,31