(10PTS!!) Find an implicit equation for the plane passing through...

Find an implicit equation for the plane passing through the points (-5,-4,0) , (-5,-9,-5) , and (0, -5, 0)

See
http://en.wikipedia.org/wiki/Plane_(geom…

ax + by + cz + d = 0

-5a - 4b + d = 0
-5a - 9b -5c + d = 0
-5b + d = 0

Let us set d=25.

-5a - 4b + 25 = 0
-5a - 9b -5c + 25 = 0
-5b + 25 = 0

Solution is
a = 1
b = 5
c = - 5

So the equation is

x + 5y - 5z + 25 = 0

-

solve the system:
ax1 + by1 + cz1 + d = 0
ax2 + by2 + cz2 + d = 0
ax3 + by3 + cz3 + d = 0

-5a - 4b + d = 0 (1)
-5a -9b - 5c + d = 0 (2)
-5b + d = 0 (3)

D = 125 (I loose a lot of time if I type the matrix of D)
Dx = - 5
Dy = -25
Dz = 25

a = -d*Dx/D = d/25
b = -d*Dy/D = d/5
c = -d*Dz/D = -d/5

for any d ≠ 0

x/25 + y/5 - z/5 + 1 = 0