1. By Prof.Dharamvirsinh Parmar

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

5.  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.  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

11.  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