Prove that the paraboloids x^2/a1^2+y^2/b1^2=2z/c1,x^2/a2^2+y^2/b2^2=2z/c2,x^2/a3^2+y^2/b3^2=2z/c3 have a common tangent plane,if |a1^2 a2^2 a3^2 | |b1^2 b2^2 b3^2 |=0? |c1 c2 c3 |
1 Answer
See below.
Explanation:
Prove that the paraboloids
have a common tangent plane, if
The normal vector to the paraboloid
If there exists a common tangent plane then
or
and analogously
this means that the columns in the matrix
are linearly dependent so