Find an equation of the sphere through the origion and whose center (1,2,3).

x^2 + y^2 + z^2 -2x - 4y - 6y = 0

Step-by-step explanation:

The equation of a sphere with centre (h, j, k) and radius r is given as

(x - h)^2 + (y - j)^2 + (z - k)^2 = r^2

r =

r = sqrt(14)

(x - 1)^2 + (y - 2)^2 + (z - 3)^2 = 14

x^2 - 2x + 1 + y^2 -4y - 4 + z^2 - 6z + 9 = 14

x^2 + y^2 + z^2 -2x - 4y - 6y + 14 = 14

x^2 + y^2 + z^2 -2x - 4y - 6y = 14 -14

x^2 + y^2 + z^2 -2x - 4y - 6y = 0

the answer is c. 23/3

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c