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
aliya0001 [1]
3 years ago
15

Write an equation for an ellipse centered at the origin, which has foci at (\pm8,0)(±8,0)left parenthesis, plus minus, 8, comma,

0, right parenthesis and vertices at (\pm17,0)(±17,0)left parenthesis, plus minus, 17, comma, 0, right parenthesis
Mathematics
1 answer:
mario62 [17]3 years ago
6 0

Answer:

The equation of the ellipse is \frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1

Step-by-step explanation:

The standard form of the equation of an ellipse with center (0 , 0) is

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 , where

  • The coordinates of the vertices are (± a , 0)  
  • The coordinates of the foci are (± c , 0) , where c ² = a² - b²  

∵ The ellipse is centered at the origin

∴ The center of it is (0 , 0)

∵ It has foci at (± 8 , 0)

- The coordinates of the foci are (± c , 0)

∴ c = ±8

∵ It has Vertices at (± 17 , 0)

- The coordinates of the vertices are (± a , 0)

∴ a = ±17

∵ c² = a² - b²

- Substitute the values of c and a to find b

∴ (8)² = (17)² - b²

∴ 64 = 289 - b²

- Add b² to both sides

∴ b² + 64 = 289

- Subtract 64 from both sides

∴ b² = 225

- Take √  for both sides

∴ b = ± 15

∵ The equation of the ellipse is \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

- Substitute the values of a and b in it

∴ \frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1 ⇒ \frac{x^{2}}{289}+\frac{y^{2}}{225}=1  

∴ The equation of the ellipse is \frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1

You might be interested in
Rachel finished 3/4 of the race in 6 hours. How long was the entire race?
s344n2d4d5 [400]
6=.75x
x= 8 hours for the whole race

5 0
3 years ago
Read 2 more answers
Plz help meeeeeeee <br>I need to turn this in today<br>plzzz!!!!!!​
Katarina [22]

Answer:



Step-by-step explanation:

Step 1 Answer: Yes, 3

Step 2 Answer: Yes, 5

Step 3 Answer: No

8 0
2 years ago
Read 2 more answers
In ΔWXY, the measure of ∠Y=90°, XW = 89, WY = 80, and YX = 39. What ratio represents the cosine of ∠X?
BartSMP [9]

Answer:

It's 39/89

Step-by-step explanation:

cos X = adjacent/ hypotenuse = 39/89

6 0
2 years ago
$43.68532 rounded to the nearest dollar is?
Sedaia [141]

Note that when rounding, if the number is:

5 or greater, round up

4 or less, round down

43.68532 rounded to the nearest dollar is 44, as 6 rounds up

$44 is your answer

hope this helps

8 0
2 years ago
205,769,205,796 + 1,784,521,794
Olin [163]

Answer:

207553727590

Step-by-step explanation:

lol lol lol lol lol lol lol

6 0
2 years ago
Read 2 more answers
Other questions:
  • Li is watering the plants in her garden. Her watering can hold 7 litres of water. She refilled the watering can 4 times. How man
    12·1 answer
  • Rebecca wants to put 544 pennies and eight coin collection book this book Fitz 9 pennies per page the red book Fitz 7 pennies pe
    15·1 answer
  • Convert 3.5 in to a fraction with 5 repeating
    9·2 answers
  • Anja is creating a triangle using three straws. The two shorter straws have lengths of 20 cm and 21 cm. How long, in centimeters
    7·1 answer
  • PLEASE HELP URGENT DO NOT WASTE ANSWERS ILL MARK YOU THE BRAINLIEST
    15·2 answers
  • Allen has four times as many cards as Bob, and Jane has twice as many cards as Allen. Together, Allen and Jane have 468 cards. H
    14·2 answers
  • Ana, Bill, and Charles are getting ready to pose for a photograph. How many different ways could they line up for the picture so
    14·2 answers
  • Children drink milk then you will be strong​
    10·2 answers
  • Can someone help I know it's easy. ( picture attached)
    6·1 answer
  • Harper bought 8.6 cm of fabric. She used 2.8 meters making a pilow . How many cm of fabric does she have left
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!