Discover the factors on the ellipsoid $x ^ 2 + 2y ^ 2 + 3z ^ 2 = 1$, where the tangent airplane is alongside the aircraft $3x - y + 3z = 1$. p I"m unsure just how to set about fixing this. I"d value some aid. p Allow the call factor be $(X, Y, Z)$, currently the tangent airplane is $$Xx +2 Yy +3 Zz=1$$ p Contrasting coefficients, $$X:2 Y:3 Z=3: -1:3$$ p That is $$\ frac =\ frac =\ frac 3Z =k$$ p Currently replace $(X, Y, Z)=\ left( 3k,-\ dfrac 2, k \ appropriate)$ right into $x ^ +2 y ^ +3 z ^ 2 =1$ p We have \ start line up * (3k)^ 2 +2 \ left( -\ frac k \ right)^ 2 +3(k)^ 2 &= 1 \ \ \ frac 25 2 k ^ &= 1 \ \ k &= \ pm \ frac 5 \ \ (X, Y, Z) &= \ left( \ pm \ frac 5, \ mp \ frac 1 , \ pm \ frac \ right)\ end straighten * p Share Point out Comply with modified Sep 27 "16 at 8:18 responded to Sep 27 "16 at 6:52 br div style="text-align: center" imager_2_6476_700.jpg" alt="*" br Ng Chung TakNg Chung Tak 17.4 k44 gold badges1616 silver badges4242 bronze badges $\ endgroup$ 9 |Program 4 b extra remarks -1 $\ begingroup$ Think about the feature $f(x, y, z) = x ^ 2 +2 y ^ 2 +3 z ^ 2-1$ then the $E$=ellipsoid is provided by $f ^ -1 (0 )$ i.e a degree surface area. Allow $p \ in E$ then $\ nabla f(p)$ is a regular vector for the tangent aircraft. For the tangent aircraft to be alongside $3x-y +3 z=1$, you require $p \ in E$ such that $\ nabla f(p) = \ lambda \ langle 3,-1,3 \ rangle$. Share Mention Adhere to modified Sep 27 "16 at 1:32 addressed Sep 27 "16 at 1:18 br baicechina.com div br Faraad ArmwoodFaraad Armwood br 8,46422 gold badges99 silver badges2121 bronze badges $\ endgroup$ 3 Include a remark| br Your Solution h2 br Many thanks for adding a solution to baicechina.comematics Heap Exchange! p Please make certain to em address the inquiry em Give information and also share your study! p Yet em prevent ... Requesting for assistance, information, or replying to various other answers.Making declarations based upon point of view; back them up with referrals or individual experience. Usage baicechina.comJax to layout formulas. baicechina.comJax recommendation. p To get more information, see our pointers on composing fantastic solutions. Draft conserved Draft disposed of br h3 Join or visit br Join making use of Google Register making use of Facebook Subscribe utilizing Email and also Password Send h3 Blog post as a visitor h3 Call Email Required, however never ever revealed br Message as a visitor h3 Call Email Called for, however never ever revealed p Blog Post Your Response Discard By clicking "Blog post Your Solution", you consent to our regards to solution, personal privacy plan and also cookie plan br Not the response you'& #x 27; re seeking? Search various other inquiries marked multivariable-calculus or ask your very own concern. Included on Meta br Connected 0 Locate tangent lines of a turned ellipse via specific factor Relevant 4 br Discovering the factors where a tangent airplane is alongside a provided aircraft? 0 Discovering the factors where a tangent aircraft is alongside an additional airplane br 0 Just how to discover factors externally $x ^ 3+y ^ 4-z ^ 3-1=0$ with tangent airplanes alongside $xy$ aircraft? br 0 Locate all the factors where the tangent aircraft is vertical to an offered vector. 0 Address for the factors on the chart where the tangent airplane is identical utilizing calculus 0 Locate the factors where a tangent airplane is alongside airplane y=0? 2 Tangent aircraft to a surface area that is alongside an additional aircraft Warm Network Questions much more warm inquiries p Concern feed Register for RSS Concern feed To register for this RSS feed, duplicate and also paste this link right into your RSS visitor. baicechina.comematics br Business br Heap Exchange Network br website style/ logo design © © 2021 Heap Exchange Inc; individual payments certified under cc by-sa. rev2021.10.19.40496 p baicechina.comematics Heap Exchange functions ideal with JavaScript allowed div Your personal privacy p By clicking "Approve all cookies", you concur Heap Exchange can keep cookies on your tool and also reveal details according to our Cookie Plan. p