1 / 13

Circles

Circles. Graphing and Writing Equations. What is a circle?. A conic formed when …. A second degree equation… A locus of points…. Definition as a conic. A circle is a conic or a conic section because it is formed by the intersection of a plane and a double-napped cone.

bayard
Télécharger la présentation

Circles

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. Circles Graphing and Writing Equations

  2. What is a circle? • A conic formed when…. • A second degree equation… • A locus of points…

  3. Definition as a conic A circle is a conic or a conic section because it is formed by the intersection of a plane and a double-napped cone.

  4. Algebraic Definition A circle is defined as the second degree equation Ax2+Bxy+Cy2 +Dx+Ey+F = 0 when A = C.

  5. A circle is a locus of points….. But, what is a locus…? A locusis the set of all points, and only those points, that satisfy one or more conditions. So, “ A locus of points in a plane 10 cm from a point A” gives a geometric description of a circle with center A and a radius of 10

  6. Geometric Definition A circle is thelocus or collection of all points (x, y) that are equidistant from a fixed point, (h, k) called the center of the circle. The distance r , between the center and any point on the circle is the radius

  7. Using the distance formula, you can derive the standard form of a circle. (x- h)2 + (y- k)2 = r 2 where, center = (h, k) and radius = r

  8. Equation of a circle: Practice Problems to write the equation of a circle when given the center and the radius.

  9. What if the center and radius are not given? • Try these : • Center = (0,3) and solution point = (0, 6) • Endpoints of diameter are (-2,3) and (6,5) • Center on the line y = 2, and tangent to the x-axis at (3,0)

  10. Graph the circle To graph a circle, locate all the points that are a fixed distance r, from the center (h, k). Click here to graph a circle

  11. Graph a circle with center at the origin Example: Graph x2 + y2 = 4

  12. To Graph a Circlecenter (h,k) and radius r Example: (x-3)2+   (y-3)2 =4 Click HereTo graph a circle if given a radius and a center

  13. What are some applications? • Circular orbits of the earth for satellites. • Perfect shape for cross-section of a submarine. • Gears • Other

More Related