Question

Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e.

Answer 1

Sol": -1 Let So, fo = 20 f = x² + y² - 2²1 ty = 2y f(12,2) f (1,2,2) (1>2,2) = 2x2 > ot fy=-22 fz (1,2,2) = -2x2 now, = 2X1 - - 4 = 2 느 4 Now, C = 0 =) Egh of tangent plane, fall.2.2) (2-1) + fylls22)(y-2) + £(123) (2-2) = 0 2 (x-1) + 4(y-2) + +7 (2-2) + 4y - X - 4+18=0 2x + 4y - 42 = 2 at zy - 22 = 1 this option - (0) And 20 -2 =) U (2) < If + oy IZ fa,y,z) ay + y² - 23 105 idf in + be jaf Ř of yi + (1+2y)] - 32² Ang option- 2 h 32 k 11