d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. Calculate the angle of rotation in degrees. f) 2. x² +24xy + 8y² + 5px + 10qy - 7 = 0
d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. Calculate the angle of rotation in degrees. f) 2. x² +24xy + 8y² + 5px + 10qy - 7 = 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 22RE
Related questions
Question
Parts D, E, and F. I attached a photo od the answers to the first three parts.
Transcribed Image Text:For each quadratic function
a) State the matrix of the quadratic form associated with the given equation.
b) Determine the eigenvalues of the matrix.
c) Construct an orthogonal matrix P with |P| = 1 that diagonalizes your matrix from a).
d) Write the equation of the function in the new coordinate system.
e) Identify the type of conic or quadric surface described by the equation.
f) Calculate the angle of rotation in degrees.
2. x² + 24xy + 8y² + 5px + 10qy - 7 = 0
![Part 3
25
978
b)
=>
=
·24 xy - 8y², 5px +10ay-700
A = [ 9 ] [ in
and 17
[-] eiser for 2018
vectr
S
12
8-
-4.
ulf u/w
6
12
-4/5
3/5
(1-2)(8-2)-144-0
7²-92-1300
(2+8)(2-17)=0
**[AR] ][ #]
PTAP=
12
ç
3/5
4/5
3/5
3 -4
2=-8
[4] For
12
E3
12
For 7=17
+25
7 = 17
4 3
25
[3388]
12. х-чусо
4v-3y=0
[2] =
7/4y
42.3
9x+12y=0
x=y
O
- 200
[58]
O
y=40
12x414y=0
22](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24638e23-7712-442e-8ea2-f441f488d4c1%2Fd5b44c62-3a65-42b5-be4d-5634836bb17b%2F6ew91wq_processed.png&w=3840&q=75)
Transcribed Image Text:Part 3
25
978
b)
=>
=
·24 xy - 8y², 5px +10ay-700
A = [ 9 ] [ in
and 17
[-] eiser for 2018
vectr
S
12
8-
-4.
ulf u/w
6
12
-4/5
3/5
(1-2)(8-2)-144-0
7²-92-1300
(2+8)(2-17)=0
**[AR] ][ #]
PTAP=
12
ç
3/5
4/5
3/5
3 -4
2=-8
[4] For
12
E3
12
For 7=17
+25
7 = 17
4 3
25
[3388]
12. х-чусо
4v-3y=0
[2] =
7/4y
42.3
9x+12y=0
x=y
O
- 200
[58]
O
y=40
12x414y=0
22
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