Question

For evaluating SJ -f(x, y, z)dx dy dz, where T is the boundary of x2 + y2 = z2, z = 4, if we
transfon Cartesian coordinates (x, y, z) into spherical polar coordinate (1,0,9), then the
limits of o will be
D
0 0 to 21
0 0 tot
0 0 to
0 0 to​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.