10.1 Conics And 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved.

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Presentation transcript:

10.1 Conics And 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved

Know the names of the conics. Objectives Know the names of the conics. Write the standard form of the equation of a circle. Graph a circle. Work with the general form of the equation of a circle. Copyright © 2013 Pearson Education, Inc. All rights reserved

Conic Sections Conic Sections are used to describe all the possible ways a plane and a double right cone can intersect. First studied in ancient Greece: 600-300 BC.

Conic Sections Circle, ellipse, parabola and hyperbola: the plane is NOT through the vertex.

Degenerate Conics Degenerate Conics: the plane DOES pass through the vertex making a point, line, or intersecting lines.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Standard Form The center is not at the origin. (x,y) r (h,k) Standard form of the equation of a circle.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Write the standard form of the equation of the circle with radius 4 and center (2, –4). Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Graph the equation Copyright © 2013 Pearson Education, Inc. All rights reserved

Find the general equation of the circle whose center is (1,–2) and whose graph contains the point (4,–2). Radius: distance from center to a point on the circle Copyright © 2013 Pearson Education, Inc. All rights reserved

Homework 1.5 #7-15 odd, 21-27 odd, 35, 37 Copyright © 2013 Pearson Education, Inc. All rights reserved