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

Excercise We have the surface work aty 1+z: 20 Soi Setelt 32 ar ay 53 500 az x The equation of of the tangent plane to the surface, = P(x,y) at ·la, b, flabl): Of (9.6) (-al + Of 196) (3-6- 24 florbloo Lo 1*2 SIER ve Aya rolan al pivita Dolore 9 YLEE 3+y*-7 P07 FO af (a,b), where point A(1,2,2) So, as I, b= l, (12. 2. af (1,2)= ay ) Now, 2x . 021 in the 1+4 - IL (,,el- by Q 3 1+4-1

: Ean. of tangent at A(1,2,2): [From ] (-1) ۰ ،(- 11 - 1 + 2 =0; .0 = 4 +27 - 4 - 2 + 1-2 د ا- 27 - 2 * و و دس