eISSN: 2349-5715
pISSN: 2349-5707
Volume: 10, Issue 12, Dec-2023
SJIF 2019: 4.702 2020: 4.737 2021: 5.071 2022: 4.919 2023: 6.980
225
Let's consider the method of constructing graphs of second-order surfaces specified by a general
equation, as well as their relative position with the plane from the geometry course using the Maple
program.
To construct a graph of a second-order surface given a general equation using the Maple program, we
need to know the order and commands for plotting in Maple.
Problem 1. Determine the relative position of the sphere with the given equation
�
�
+ �
�
+
�
�
= �
, and the plane
�� + �� − � = �
:
>with(plots): implicitplot3d([x^2+y^2+z^2=1,2*x+3*y-z=0], x=-1..1, y=-1..1, z=-1..1);
Figure 1. Intersection of a sphere and a plane
Problem 2. Determine the relative position of the ellipsoid
�
�
+ ��
�
+ ��
�
−
� = �
and the plane
�� + � + � = �
:
>with(plots):
implicitplot3d([x^2+2*y^2+3*z^2=1,2*x+y+z=0], x=-1..1, y=-1..1, z=-1..1);
Figure 1. Intersection of an ellipsoid and a plane
Problem 3. Determine the relative position of the hyperboloid
�
�
�
+
�
�
�
−
�
�
�
= �
and the plane
� + �� − � = �
:
eISSN: 2349-5715
pISSN: 2349-5707
Volume: 10, Issue 12, Dec-2023
SJIF 2019: 4.702 2020: 4.737 2021: 5.071 2022: 4.919 2023: 6.980
226
>with(plots):
implicitplot3d([x^2/3+y^2/5-z^2/2=1,x+3*y-z=0], x=-5..5, y=-5..5, z=-4..4);
Figure 3. Intersection of a hyperboloid and a plane
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