1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vikentia [17]
3 years ago
11

Write and equation of the translated or rotated graph in general form (picture below)

Mathematics
2 answers:
WINSTONCH [101]3 years ago
6 0

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

 xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

  the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ (\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=

 ( \frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0

* Lets open the bracket

∴ \frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0

* Lets add the like terms

∴ \frac{-4xy}{2}-16=0

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

Bogdan [553]3 years ago
3 0

Answer:

a. hyperbola;

You might be interested in
Which phrase best defines a trapezoid?
balu736 [363]
B they only have one pair of parallel sides. The top and bottom
3 0
3 years ago
Read 2 more answers
Which annual subscription costs the most ?
Juli2301 [7.4K]

Answer:

fun for kids and family fun

Step-by-step explanation:

7 0
3 years ago
What is tan 330°? for algebra 2 with trig in it.
Alekssandra [29.7K]
Tan (330) = 0.133557
8 0
3 years ago
Given f(x) =3x-7, find f(x+1)+f(1)
ELEN [110]

Answer:

3x - 8

Step-by-step explanation:

To find f(x + 1) substitute x = x + 1 into f(x)

f(x + 1) = 3(x + 1) - 7 = 3x + 3 - 7 = 3x - 4

Similarly

f(1) = 3(1) - 7 = 3 - 7 = - 4

Hence

f(x + 1) + f(1) = 3x - 4 - 4 = 3x - 8

3 0
3 years ago
there are 18 boys and 12 girl in math class. what is the ratio of girls to total students. A. 18:30 B. 12:30 C. 30:12 D. 30:18 2
zmey [24]

Answer:

1.  B

2. B and C

3.C

4.B the answer is 238 but i guess the rounded

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Find the 25th of sequence 3,5,7,9,11
    5·1 answer
  • T what point does the curve have maximum curvature? Y = 7ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as
    13·1 answer
  • What is the next term of the geometric sequence?<br> 54,36,24...
    14·1 answer
  • Janice bought 40 shares of stock at $31.82 per share. She received dividends of $1.11 per share for 1 year. What was her purchas
    5·2 answers
  • a solid circular cylinder of radius 7 cm and length 8 cm is made out of metal alloy. given that 1 cm³ of the alloy has a mass of
    11·1 answer
  • If the simple inttrest on $ 2.000 for 2 years then what is the intrest rate
    8·1 answer
  • An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice
    10·1 answer
  • Which is bigger 3.2 or 3.23
    8·2 answers
  • A delivery truck has 40,000 miles on its odometer and travels an average of 22,000 miles per year.
    10·1 answer
  • PLEASE PLEASE HELP ME
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!