Let us suppose that the coordinate aves in xy system is rotated through an angle 'A' to form x'y' system. Then, We have the following relations : сово -sino7 [i] = [][*] Sino Coso у i.e. x = x² cosa - y'sino and y=x'sino + y² COA O 1 Solution: Given equation is 8x²-24xy + 15y² + 4y -4 = 0 −(1) Comparing (1) ax² + 2 hxy + by² + 2gx + 2 fy + c = 0 (ii) We have, (1) with the equation 9=8₁ h = -121 6=15 ô h² = (-12)² = 144 and ab=120 :: h²_ab= 144-120=2470 i. ĥ² yab Thus, (1) represents a [hyperbola - Answer
Let us suppose that the coordinate aves in xy system is rotated through an angle 'A' to form x'y' system. Then, We have the following relations : сово -sino7 [i] = [][*] Sino Coso у i.e. x = x² cosa - y'sino and y=x'sino + y² COA O 1 Solution: Given equation is 8x²-24xy + 15y² + 4y -4 = 0 −(1) Comparing (1) ax² + 2 hxy + by² + 2gx + 2 fy + c = 0 (ii) We have, (1) with the equation 9=8₁ h = -121 6=15 ô h² = (-12)² = 144 and ab=120 :: h²_ab= 144-120=2470 i. ĥ² yab Thus, (1) represents a [hyperbola - Answer
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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![Let us suppose that the coordinate aves in xy system is
rotated through angle 'O' to form x'y' system. Then,
an
We have the following relations :
Sino
[i] = [tex][*]
у
x = x² cosa - y'sino and y=x'sino + y/cos@
i.e.
Solution:
We have,
Given
qquation is
82² - 24 xy + 15y² + 4y -4 = 0 −0)
Comparing (1)
(1) with the equation
ax² + ²xy + by² + 2gx + 2 fy+ c = 0 (ii)
2hxyt
Sino
9=8₁ h=-121 6=15
öz ĥ² = (-12)² = 144 and ab = 120
:: h²_ab= 144-120=2470
: 12>ab
Thus, (i) represents a hyperbola
We know that
tan (20) = 2h
.:
tan (20) = -24
Also, coxo =
сово =
and
a-b
7
clearly, Cos (20) = 25
Also,
sino =
sino = 1/2/3/4
.:
8-15
Using Calculater 0~36.86
Now, use the formulne to find sino, coso.
=
lcos(20)
2
x²
1+ (08(20)
4
5
24
7
y
=
=
Answer
1+ 7/1/15
25
2
1-7/5
25
2
зу
x = x² C080 - Y'sino = 4x² - 34' 5
5
5
"
=
x² sino + y'coso = 3x² + + ² = 1 (3x² + 4 y²)
y =
5
putting the value
of x and
in (i)
-5x1² + 120y₁² + 12x1² + 16y² = 20 = 0
= —— (4x² - 3y²)
=
18
2x25
32
2x25
we have,
Answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4be50db6-19e4-41fe-8b0c-6d619944736f%2F78522cac-a1bd-457d-86c2-4aee0cb2cd2f%2Fu9bc59p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let us suppose that the coordinate aves in xy system is
rotated through angle 'O' to form x'y' system. Then,
an
We have the following relations :
Sino
[i] = [tex][*]
у
x = x² cosa - y'sino and y=x'sino + y/cos@
i.e.
Solution:
We have,
Given
qquation is
82² - 24 xy + 15y² + 4y -4 = 0 −0)
Comparing (1)
(1) with the equation
ax² + ²xy + by² + 2gx + 2 fy+ c = 0 (ii)
2hxyt
Sino
9=8₁ h=-121 6=15
öz ĥ² = (-12)² = 144 and ab = 120
:: h²_ab= 144-120=2470
: 12>ab
Thus, (i) represents a hyperbola
We know that
tan (20) = 2h
.:
tan (20) = -24
Also, coxo =
сово =
and
a-b
7
clearly, Cos (20) = 25
Also,
sino =
sino = 1/2/3/4
.:
8-15
Using Calculater 0~36.86
Now, use the formulne to find sino, coso.
=
lcos(20)
2
x²
1+ (08(20)
4
5
24
7
y
=
=
Answer
1+ 7/1/15
25
2
1-7/5
25
2
зу
x = x² C080 - Y'sino = 4x² - 34' 5
5
5
"
=
x² sino + y'coso = 3x² + + ² = 1 (3x² + 4 y²)
y =
5
putting the value
of x and
in (i)
-5x1² + 120y₁² + 12x1² + 16y² = 20 = 0
= —— (4x² - 3y²)
=
18
2x25
32
2x25
we have,
Answer.
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