1 / 14

CONICOIDE

CONICOIDE. By Prof.Dharamvirsinh Parmar. Definition. The locus of the general equation of second degree in x, y, z is called a conicoid or quadric . . Ellipsoid. Properties. It is clear that centre of ellipsoid is (0, 0 0) Symmetrical with respect to three co – ordinate axis.

brent
Download Presentation

CONICOIDE

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. CONICOIDE By Prof.DharamvirsinhParmar

  2. Definition • The locus of the general equation of second degree in x, y, z is called a conicoid or quadric . DHARAMVIRSINH PARMAR

  3. Ellipsoid DHARAMVIRSINH PARMAR

  4. DHARAMVIRSINH PARMAR

  5. Properties • It is clear that centre of ellipsoid is (0, 0 0) • Symmetrical with respect to three co – ordinate axis. • Point of intersection with X – axis are (a,0,0) and (-a,0,0). • Similarly intersection with Y – axis, Z - axis are (0,±b,0) and (0,0, ±c) respectively. • For any point (x, y, z) on ellipsoid, -a ≤ x ≤ a, -b ≤ y ≤ b and –c ≤ z ≤ c. Ellipsoid is symmetrical surface. • The section of the surface by the plane z = k which are parallel to XOY plane are similar ellipses having equation DHARAMVIRSINH PARMAR

  6. Hyperboloid Of One Sheet

  7. DHARAMVIRSINH PARMAR

  8. Properties • It is clear that centre of Hyperboloid of one sheet is (0, 0 0) • Symmetrical with respect to three co – ordinate axis. • Point of intersection with X – axis are (a,0,0) and (-a,0,0). • Similarly intersection with Y – axis are (0,±b,0). • It will not intersect to Z – axis, for that put x = 0, y = 0, we get z = - which is not possible • The section of the surface by the plane z = k which are parallel to XOY plane are similar ellipses having equation DHARAMVIRSINH PARMAR

  9. Hyperboloid of two sheet DHARAMVIRSINH PARMAR

  10. DHARAMVIRSINH PARMAR

  11. Properties • It is clear that centre of Hyperboloid of two sheet is (0, 0 0) • Symmetrical with respect to three co – ordinate axis. • Point of intersection with X – axis are (a,0,0) and (-a,0,0). • It will not intersect to Y-axis and Z – axis. • The section of the surface by the plane z = k which are parallel to XOY plane are similar hyperbolas having equation • The plane x = k, does not meet surface if • There is no portion of the surface between x = -a to x = a DHARAMVIRSINH PARMAR

  12. Elliptic Paraboloid DHARAMVIRSINH PARMAR

  13. DHARAMVIRSINH PARMAR

  14. Hyperbolic Paraboloid DHARAMVIRSINH PARMAR

More Related