Tutorial 9 Tangency 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