mathstina
At what point on the paraboloid y = x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1?
Delete
Share
This Question is Closed
TuringTest
Best Response
You've already chosen the best response.
2
find the gradient of the surface
mathstina
Best Response
You've already chosen the best response.
0
<2,-1,2>
TuringTest
Best Response
You've already chosen the best response.
2
grad f=<2x, -1, 2z>
mathstina
Best Response
You've already chosen the best response.
0
yes
TuringTest
Best Response
You'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 j-component equal to 2 like it is for the plane
mathstina
Best Response
You've already chosen the best response.
0
multiply by -2
TuringTest
Best Response
You've already chosen the best response.
2
right, and so we get?
mathstina
Best Response
You've already chosen the best response.
0
grad f=<-4x,2y, -4z>
TuringTest
Best Response
You've already chosen the best response.
2
grad f=<-4x,2,-4z>
that y can't just appear from nowhere
TuringTest
Best Response
You've already chosen the best response.
2
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?
mathstina
Best Response
You've already chosen the best response.
0
x=1/2and z= 3/2 ???
TuringTest
Best Response
You've already chosen the best response.
2
from the equation as we have it we need x=-1/4 and z=-3/4
mathstina
Best Response
You've already chosen the best response.
0
ok.
TuringTest
Best Response
You've already chosen the best response.
2
that's all then... boring problem
mathstina
Best Response
You've already chosen the best response.
0
why qns with sphere have 2 sets of points?
TuringTest
Best Response
You've already chosen the best response.
2
hm... seems strange that y does not matter. Maybe I messed this one up :P
TuringTest
Best Response
You've already chosen the best response.
2
sorry? what do you mean?
mathstina
Best Response
You've already chosen the best response.
0
for qns with sphere has 2 sets of points as ans why?
TuringTest
Best Response
You've already chosen the best response.
2
what do you mean it has 2 sets of points?
mathstina
Best Response
You've already chosen the best response.
0
the ans fot this qn is (-1/4, -2,-3/4)
TuringTest
Best Response
You'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
mathstina
Best Response
You've already chosen the best response.
0
so the point for y is 0 or -1?
TuringTest
Best Response
You've already chosen the best response.
2
neither, the result says y can be anything, so just write y=y
amistre64
Best Response
You'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