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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?
 one year ago
 one year ago
At what point on the paraboloid y = x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1?
 one year ago
 one year ago

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TuringTestBest ResponseYou've already chosen the best response.2
find the gradient of the surface
 one year ago

TuringTestBest ResponseYou've already chosen the best response.2
grad f=<2x, 1, 2z>
 one year ago

TuringTestBest 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
 one year ago

TuringTestBest ResponseYou've already chosen the best response.2
right, and so we get?
 one year ago

mathstinaBest ResponseYou've already chosen the best response.0
grad f=<4x,2y, 4z>
 one year ago

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

TuringTestBest 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?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.2
from the equation as we have it we need x=1/4 and z=3/4
 one year ago

TuringTestBest ResponseYou've already chosen the best response.2
that's all then... boring problem
 one year ago

mathstinaBest ResponseYou've already chosen the best response.0
why qns with sphere have 2 sets of points?
 one year ago

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

TuringTestBest ResponseYou've already chosen the best response.2
sorry? what do you mean?
 one year ago

mathstinaBest ResponseYou've already chosen the best response.0
for qns with sphere has 2 sets of points as ans why?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.2
what do you mean it has 2 sets of points?
 one year ago

mathstinaBest ResponseYou've already chosen the best response.0
the ans fot this qn is (1/4, 2,3/4)
 one year ago

TuringTestBest 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
 one year ago

mathstinaBest ResponseYou've already chosen the best response.0
so the point for y is 0 or 1?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.2
neither, the result says y can be anything, so just write y=y
 one year ago

amistre64Best 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
 one year ago
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