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
Arada [10]
3 years ago
13

write an equation for an ellipse centered at the origin which has foci at (0,±√14) and co-vertices at (±√2,0)

Mathematics
1 answer:
gregori [183]3 years ago
5 0

Answer:

The answer to your question is   \frac{x^{2} }{2} + \frac{y^{2} }{16} = 1

Step-by-step explanation:

Data

F ( 0, ± √14)

C (±√2, 0)

Process

1.- Calculate c

c is the distance from the center to the foci

c = √14

2.- Calculate b

b is the distance from the center to the co-vertices

b = √2

3.- Calculate a using the Pythagorean theorem

     a² = b² + c²

     a² = (√2)² + (√14)²

     a² = 2 + 14

     a² = 16

     a = 4

4.- We can conclude that it is a vertical ellipse because the foci are in the y- axis and the co-vertices are in the x-axis.

          (x - h)²/b² + (y - k)²/a² = 1

-Substitution

          (x - 0)²/(√2)² + (y - 0)²/4² = 1

- Simplification

          x²/2 + y²/16 = 1

or    \frac{x^{2} }{2} + \frac{y^{2} }{16} = 1

You might be interested in
-5x^2-6=-4x using the Quadratic Formula.
a_sh-v [17]

Answer:

Step-by-step explanation:

-5x² - 6 = -4x

-5x² + 4x - 6 = 0

a = -5  ; b = 4  ; c = -6

Discriminant = b² - 4ac

                     = 4² - 4*(-5)*(-6)

                     = 16 - 120

                     = -104

roots = \dfrac{-b+\sqrt{D}}{2a} \ ; \   \dfrac{-b-\sqrt{D}}{2a}

=\dfrac{-4+\sqrt{-104}}{2*(-5)};\dfrac{-4-\sqrt{-104}}{2*(-5)}\\\\=\dfrac{-4+2i\sqrt{26}}{-10} ; \dfrac{-4-2i\sqrt{26}}{-10}\\\\=\dfrac{(-2)[2-i\sqrt{26}]}{-10} \ ; \ \dfrac{(-2)[2+i\sqrt{26}]}{-10}\\\\=\dfrac{2-i\sqrt{26}}{5} \ ; \ \dfrac{2+i\sqrt{26}}{5}

5 0
3 years ago
The bottom of a rectangular swimming pool has a perimeter of 62 meters. Its area is 220 square meters. What are the dimensions o
Dahasolnce [82]

Answer:

13640cubicmeter........

6 0
2 years ago
Consider the graph of the cosine function shown below.
emmainna [20.7K]

Answer:

a. The amplitude should be 2.

   The period should be 2\pi.

b. maximum value occurs in (0,1) at x = 0

    minimum value occurs in (pi,-1) at x = pi

Step-by-step explanation:

8 0
2 years ago
Can someone help me with this please
8_murik_8 [283]

Answer: 360 ft squared

Step-by-step explanation:

3 0
3 years ago
Which statements are true about exponential decay functions check all that apply
melomori [17]
This is the concept of exponential functions; The statements that are correct about the exponential decay functions are:
1. The domain is all real number
4. The base must be less than 1 and greater than 0
5. The function has a constant multiplicative rate of change
3 0
3 years ago
Read 2 more answers
Other questions:
  • How much interest would a bond (1,000 shares) of RMx pay each year?
    7·2 answers
  • The temperature is 15 degrees and is expected to fall 2 degrees each hour during the night.write the linear equation that models
    10·2 answers
  • X(4-k)=p solve for k<br><br><br> I can't figure out how please help
    12·1 answer
  • To find the product of 42.12 and 10³, move the decimal point in 42.12 __ places to the right because 10³ has __ zeros.
    8·2 answers
  • How do I find the quotient 7/8÷2/9
    7·2 answers
  • There are 50 students that voted for new sports and 6 voted for rugby what is the percentage
    12·2 answers
  • Help help me please
    6·1 answer
  • PLEASE HELP ME WITH THESE TWO PROBLEMS ASAP !!!!!!! PLS
    14·2 answers
  • Help me pleaseeeeeeee​
    7·1 answer
  • Help pleaseeeeeeeeeeeee
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!