In: Advanced Math
Show that the surfaces are tangent to each other at the given point by showing that the surfaces have the same tangent plane at this point. x2 + y2 + z2 − 20x − 16y + 2z + 115 = 0, x2 + y2 + 6z = 17, (5, 4, −4)
Both surfaces have the tangent plane of (answer )
at (5, 4, −4), therefore they are tangent to each other at this point.