Consider the ellipsoid x² + y² + 4 (a) Carefully graph the ellipsoid. (b) The point (-2, 1, −3) is on this ellipsoid. Use the normal vector find a equation of the plane at the point (-2, 1, −3) with normal n. (c) Find the distance from (-2, 1, -3) to the plane you gave. Find any other point on the plane you gave in part b.) and find the distance from that point to the point (-2, 1, -3). =(-1,2,-²), =
Consider the ellipsoid x² + y² + 4 (a) Carefully graph the ellipsoid. (b) The point (-2, 1, −3) is on this ellipsoid. Use the normal vector find a equation of the plane at the point (-2, 1, −3) with normal n. (c) Find the distance from (-2, 1, -3) to the plane you gave. Find any other point on the plane you gave in part b.) and find the distance from that point to the point (-2, 1, -3). =(-1,2,-²), =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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calculus
Transcribed Image Text:x²
4
(a) Carefully graph the ellipsoid.
(b) The point (–2, 1, −3) is on this ellipsoid. Use the normal vector ñ = (-1,2,-²),
3
find a equation of the plane at the point (-2, 1, -3) with normal n.
(c) Find the distance from (-2, 1, −3) to the plane you gave. Find any other point
on the plane you gave in part b.) and find the distance from that point to the
point (-2, 1, -3).
5. Consider the ellipsoid
+ y² +
(e) The vector, ñ
=
9
(d) Give two more points that are on the ellipsoid.
x
(1/12
2z
gives the normal vector to any point (x, y, z) that
9
lies on the ellipsoid. Using this normal vector ñ, find an equation of the plane at
each point on the ellipsoid you found in part d.).
24,
= 3.
=
"
(f) Give a rough sketch of each plane you gave in part e.) on the ellipsoid that you
graphed in part a.)
Expert Solution
Step 1
We will standardize the equation given and then will find graph of it . For equation of plane we will use
Note : Maximum three sub part are allowed to be solved at a time . For other parts please repost .
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