First tutorial on Sphere: In the present tutorial, we discuss about the definition of the sphere, equations of the sphere, equation of sphere in standard form, equations of sphere in central form and equation of sphere in general. How can we find the center and radius of a sphere given in general form

1. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Tutorial-I: Sphere
Analytic Geometry: Sphere
Dr. Mehar Chand
Department of Mathematics
Baba Farid College, Bathinda-151001
April 13, 2020
Dr. Mehar Chand Analytic Geometry: Sphere

2. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Contents
1 Definition of the Sphere
Equation of sphere in standard form
Equation of sphere in Central form
Equation of sphere in General form
2 Some problems related to any sphere through the circle
3 Full video Lecture
Dr. Mehar Chand Analytic Geometry: Sphere

3. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Definition of the Sphere
Art. (Definition of the Sphere)
A sphere is the locus of a point, which moves in space so
that its distance from a fixed point is constant. The fixed
point is called the centre and the constant distance is called
radius of the sphere.
Dr. Mehar Chand Analytic Geometry: Sphere

4. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Equation of sphere in standard form
Art. (Equation of sphere in standard form)
Show that the equation of the sphere whose centre is origin
and radius is a is given by
x2
+ y2
+ z2
= a2
Dr. Mehar Chand Analytic Geometry: Sphere

5. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Equation of sphere in Central form
Art. (Equation of sphere in Central form)
Find the equation of the sphere, whose centre and radius
are given
Dr. Mehar Chand Analytic Geometry: Sphere

6. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Equation of sphere in General form
Art. (Equation of sphere in General form)
Prove that the equation
x2
+ y2
+ z2
+ 2ux + 2vy + 2wz + d = 0
represent a sphere. Also find the its centre and radius.
Dr. Mehar Chand Analytic Geometry: Sphere

7. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Any sphere through the circle
Example (1)
Obtain the equation of the sphere, whose centre is
(1, −1, 1) and whose radius is the same as that of the
sphere 2x2 + 2y2 + 2z2 − 2x + 4y − 6z = 1.
Example (2)
One end of a diameter of the sphere
x2 + y2 + z2 − 6x − 12y − 2z + 20 = 0 is (2, 3, 5), find the
other end of the diameter.
Dr. Mehar Chand Analytic Geometry: Sphere

8. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Any sphere through the circle
Example (3)
A point moves so that the sum of the squares of its distance
from the six faces of a cube is (a positive) constant;, show
that its locus is a sphere.
Example (4)
A plane is passing through a fixed point (a, b, c). Show that
the locus of the foot of perpendicular to it from the origin is
the sphere x2 + y2 + z2 − ax − by − cz = 0
Dr. Mehar Chand Analytic Geometry: Sphere

9. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Full video Lecture
To see full video lecture visit the below link
https://www.youtube.com/watch?v=tTfwnODqsMU&
feature=youtu.be
Dr. Mehar Chand Analytic Geometry: Sphere

10. Analytic
Geometry:
Sphere
Dr. Mehar
Chand
Definition
Standard form
Central form
General form
Problems
Video
Thank you
Dr. Mehar Chand Analytic Geometry: Sphere