Question

Please show step by step how they got (1-4+(9/2))k^2 = 1 on the last line.

Find the points on the hyperboloid x2 - y2 + 2z2 = 1 where the normal line is parallel to the line that joins the points (3,-1,0) and (5,3,6).

Answer 1

Solutions f(x,y,z)= 22532 te = za fy=-2y fz= 47 Vf = (27,-27,42). let (xo, Yoito) be the pt. where normal line is parallel to the line that joins the given points (3, 1,0) and (.5; 3,6) The direction no. joining these points = {2,4,67 → <2x69-2409 477- k <2,4,67 = %=k , 4o = -2K,76= Ķk - Now (2o, Yo, Zo) lies on hyperboloid. Hence will satisfy : * x²_y² + 2 to » K²_4K ²+ 2/3 = 1 5 (1–4+2x9)k=;

(1-4+2)= == K* + » points are | Pergy 3)=( 1-17,三) ( -2 ,3) 7 psy) (一度,+1, ) (三 )如