anonymous
  • anonymous
At what point on the paraboloid y = x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1?
Mathematics
schrodinger
  • schrodinger
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TuringTest
  • TuringTest
find the gradient of the surface
anonymous
  • anonymous
<2,-1,2>
TuringTest
  • TuringTest
grad f=<2x, -1, 2z>

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anonymous
  • anonymous
yes
TuringTest
  • TuringTest
ok, now since we can't plug in anything that will change y, let's multiply the gradient by a scalar to get the j-component equal to 2 like it is for the plane
anonymous
  • anonymous
multiply by -2
TuringTest
  • TuringTest
right, and so we get?
anonymous
  • anonymous
grad f=<-4x,2y, -4z>
TuringTest
  • TuringTest
grad f=<-4x,2,-4z> that y can't just appear from nowhere
TuringTest
  • TuringTest
so what value of x makes the i-components equal for the plane and grad f ? what value of z makes the k-components equal?
anonymous
  • anonymous
x=1/2and z= 3/2 ???
TuringTest
  • TuringTest
from the equation as we have it we need x=-1/4 and z=-3/4
anonymous
  • anonymous
ok.
TuringTest
  • TuringTest
that's all then... boring problem
anonymous
  • anonymous
why qns with sphere have 2 sets of points?
TuringTest
  • TuringTest
hm... seems strange that y does not matter. Maybe I messed this one up :P
TuringTest
  • TuringTest
sorry? what do you mean?
anonymous
  • anonymous
for qns with sphere has 2 sets of points as ans why?
TuringTest
  • TuringTest
what do you mean it has 2 sets of points?
anonymous
  • anonymous
the ans fot this qn is (-1/4, -2,-3/4)
TuringTest
  • TuringTest
the way we did it it looks like y does not matter, so (-1/4,y,-3/4) seems strange that y does not matter though, maybe I made a mistake... not sure
anonymous
  • anonymous
so the point for y is 0 or -1?
TuringTest
  • TuringTest
neither, the result says y can be anything, so just write y=y
amistre64
  • amistre64
isnt y a function if x and z to begin with? y = x^2 + z^2; therefore y=1/4

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