condition of Tangency of Line and Sphere, Locus of point of contact of line and sphere

1. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Tutorial-IX: Sphere
Tangency of Line and
Sphere
Dr. Mehar Chand
Department of Mathematics
Baba Farid College, Bathinda-151001
April 20, 2020
Dr. Mehar Chand Tangency of Line and Sphere

2. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Contents
1 Condition of Tangency
2 Locus of point of contact of tangent plane to the Sphere
3 Diametral plane property
4 Some problems are discussed in this section
5 Full video Lecture
Dr. Mehar Chand Tangency of Line and Sphere

3. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Condition of Tangency of Line and Sphere
Art. (Condition of Tangency of Line and Sphere)
Find the condition that the line
x − x1
l
=
y − y1
m
=
z − z1
n
may touch the sphere
x2
+ y2
+ z2
= a2
Dr. Mehar Chand Tangency of Line and Sphere

4. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Condition of Tangency of Line and Sphere
Art. (Condition of Tangency of Line and Sphere)
Find the condition that the line
x − x1
l
=
y − y1
m
=
z − z1
n
may touch the sphere
x2
+ y2
+ z2
+ 2ux + 2vy + 2wz + d = 0
Dr. Mehar Chand Tangency of Line and Sphere

5. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Locus of point of contact of tangent plane
to the Sphere
Art. (Locus of point of contact of tangent plane to the
Sphere)
Find the locus of point of contact of tangent plane to the
Sphere x2 + y2 + z2 = a2, which pass through a given point
(x1, y1, z1).
Dr. Mehar Chand Tangency of Line and Sphere

6. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Diametral plane property
Art. (Diametral plane property)
Find the locus of the middle points of a system of parallel chords
of a sphere.
Note (Diametral Plane)
The locus of the mid-points of a system of parallel chords of a
sphere is a plane called a diametral plane
Note (Equation of Diametral Plane)
Let the equation of the sphere be
F(x, y, z) = x2 + y2 + z2 − a2 = 0, then the equation of the
diametral plane is
l
∂F
∂x
+ m
∂F
∂y
+ n
∂F
∂z
= 0
Dr. Mehar Chand Tangency of Line and Sphere

7. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Some questions
Q-1 Prove that the centre of the sphere which touch the
lines y = mx, z = c; y = −mx, z = −c lies upon the
conicoid mxy + cz(1 + m2) = 0
Q-2 Show that the line
x − 7
2
=
y − 4
7
=
z − 13
10
touch the sphere
s : x2
+ y2
+ z2
− 6x + 2y − 4z + 5 = 0
Find the co-ordinate of P, the point of contact.
Dr. Mehar Chand Tangency of Line and Sphere

8. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Full video Lecture
To see full video lecture visit the below link
https://youtu.be/rtO2bnVPUic
Dr. Mehar Chand Tangency of Line and Sphere

9. Tangency of
Line and
Sphere
Dr. Mehar
Chand
Condition of
Tangency
Locus of point
of contact
Diametral
Problems
Video
Thank you
Dr. Mehar Chand Tangency of Line and Sphere