Can I have a detailed explanation for the part (a) part of the following question? Thank you very much! (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoidAr? + By? + cz? = 1 at the point (a, B, 7).(b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at thepoint (1, -1, 1).(c) Show that the plane 3r+12y-6z = 17 touches the hyperboloid 3x2 -6y?+922+17 = 0and find the point of contact.

Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Answered: (a) Obtain the equation of the tangent…

(a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? + By? + cz2 = 1 at the point (a, B, y). %3D

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Can I have a detailed explanation for the part (a) part of the following question?

Thank you very much!

(a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid
Ar? + By? + cz? = 1 at the point (a, B, 7).
(b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the
point (1, -1, 1).
(c) Show that the plane 3r+12y-6z = 17 touches the hyperboloid 3x2 -6y?+922+17 = 0
and find the point of contact.

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