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mathstina
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At what point on the paraboloid y = x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1?
 2 years ago
 2 years ago
mathstina Group Title
At what point on the paraboloid y = x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1?
 2 years ago
 2 years ago

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TuringTest Group TitleBest ResponseYou've already chosen the best response.2
find the gradient of the surface
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
grad f=<2x, 1, 2z>
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
ok, now since we can't plug in anything that will change y, let's multiply the gradient by a scalar to get the jcomponent equal to 2 like it is for the plane
 2 years ago

mathstina Group TitleBest ResponseYou've already chosen the best response.0
multiply by 2
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
right, and so we get?
 2 years ago

mathstina Group TitleBest ResponseYou've already chosen the best response.0
grad f=<4x,2y, 4z>
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
grad f=<4x,2,4z> that y can't just appear from nowhere
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
so what value of x makes the icomponents equal for the plane and grad f ? what value of z makes the kcomponents equal?
 2 years ago

mathstina Group TitleBest ResponseYou've already chosen the best response.0
x=1/2and z= 3/2 ???
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
from the equation as we have it we need x=1/4 and z=3/4
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
that's all then... boring problem
 2 years ago

mathstina Group TitleBest ResponseYou've already chosen the best response.0
why qns with sphere have 2 sets of points?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
hm... seems strange that y does not matter. Maybe I messed this one up :P
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
sorry? what do you mean?
 2 years ago

mathstina Group TitleBest ResponseYou've already chosen the best response.0
for qns with sphere has 2 sets of points as ans why?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
what do you mean it has 2 sets of points?
 2 years ago

mathstina Group TitleBest ResponseYou've already chosen the best response.0
the ans fot this qn is (1/4, 2,3/4)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
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
 2 years ago

mathstina Group TitleBest ResponseYou've already chosen the best response.0
so the point for y is 0 or 1?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
neither, the result says y can be anything, so just write y=y
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
isnt y a function if x and z to begin with? y = x^2 + z^2; therefore y=1/4
 2 years ago
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