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
Mice21 [21]
3 years ago
15

Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

Mathematics
1 answer:
NemiM [27]3 years ago
6 0

Answer:

x squared over 4 plus y squared over 8 equals 1

Step-by-step explanation:

The general equation of ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

You might be interested in
14 POINTS 7x - 3 = 18
Svetlanka [38]
Subtract 3 first so it would be 7x=15
then divide by 7 so x would be approximately 2.14
5 0
3 years ago
Read 2 more answers
Find the area of this question
oee [108]
The answer to this question whould be that the area is 20
7 0
3 years ago
A coin is tossed 5 times. Find the probability that all are heads. Find the probability that at most 2 are heads.
fenix001 [56]

Answer:

1/32

15/32

Step-by-step explanation:

For a fair sided coin,

Probability of heads, P(H) = 1/2

Probability of tails P(T)  = 1/2

For a coin tossed 5 times,

P( All heads)

= P(HHHHH),

= P (H) x P(H) x P(H) x P(H) x P(H)

= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/32 (Ans)

For part B, it is easier to just list the possible outcomes for

"at most 2 heads" aka "could be 1 head" or "could be 2 heads"

"One Head" Outcomes:

P(HTTTT), P(THTTT) P(TTHTT), P(TTTHT), P(TTTTH)

"2 Heads" Outcomes:

P(HHTTT), P(HTHTT), P(HTTHT), P(HTTTH), P(THHTT), P(THTHT), P(THTTH), P(TTHHT), P(TTHTH), P(TTTHH)

If we count all the possible outcomes, we get 15 possible outcomes representing "at most 2 heads)

we know that each outcome has a probability of 1/32

hence 15 outcomes for "at most 2 heads" have a probability of

(1/32) x 15  = 15/32

8 0
3 years ago
Read 2 more answers
Write the equation of the line that has a slope of 2/3 and passes through (0,-7).
likoan [24]
The equation of the line is (slope-intercept) y=\frac{2}{3}x+(-7) or (standard form) \frac{-2}{3}x+y=-7
6 0
4 years ago
What kind of angle is this and how do you work it out?
Lostsunrise [7]
Well x is an obtuse angle

but the angle e,f,g is an acute angle
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the mean median and mode of 99, 69, 96, 69, 78. Round to the nearest tenth if necessary
    15·1 answer
  • Points<br>Which values should you plot to show a linear relationship?​
    8·1 answer
  • If tan 0=5/4, calculate the value of cos 0
    13·1 answer
  • What are the equivalent ratios?​
    9·1 answer
  • P(n)=n^2-5n; find p(-3)
    15·1 answer
  • I need help with these questions (see image). Please show workings.<br>​
    12·2 answers
  • 4. Written as the product of two binomials, the expression (x+3)(4x –1)-(x+3)(x –9) is
    11·1 answer
  • Helpppp I’m literally so confused
    13·2 answers
  • Help :)))))))))))))))))))))))))))))
    14·2 answers
  • ‼️‼️‼️‼️HELP‼️‼️‼️‼️‼️‼️‼️
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!