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

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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2ok, 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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