1 / 9

Conic Sections

Conic Sections. Circle. Conics. Four Basic Conic Shapes: Circle Parabola Ellipse Hyperbola A conic section (or simply conic ) is the intersection of a plane and a double-napped cone. When the plane does pass through the vertex, the resulting figure is a degenerate conic. Conics.

quana
Télécharger la présentation

Conic Sections

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Conic Sections Circle

  2. Conics • Four Basic Conic Shapes: • Circle • Parabola • Ellipse • Hyperbola • A conic section (or simply conic) is the intersection of a plane and a double-napped cone. • When the plane does pass through the vertex, the resulting figure is a degenerate conic.

  3. Conics • Geometrically, each conic is defined as a locus (collection) of points satisfying a geometric property. • Algebraically, each conic is given by a general second-degree equation: • Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 • But in our class, most of time, B = 0, so: • Ax2 + Cy2 + Dx + Ey + F = 0

  4. Circle • A circle is the set of all points in a plane that are a fixed distance r (called the radius) from a fixed point (called the center). • Vocabularies: • Center • Radius • Diameter • Standard Form of a Circle: • (x – h)2 + (y – k)2 = r2 • Center: (h, k) • Radius = r

  5. Practice Problem • Find the equation of the circle with center (–2, 1) and radius 3. • (x+2)2 + (y–1)2 = 9 (Standard Form) • x2 + y2 + 4x – 2y – 4 = 0 (General Form)

  6. Practice Problem • Find the equation of the circle with center (3, 5) and tangent to the y-axis.

  7. Practice Problem • Write the equation of a circle if the endpoints of a diameter are at (5, 4) and (–1, –2).

  8. Carb: x2 + y2 = infinity2 Fin…

More Related