Mathematics, 07.08.2019 18:30 jwdblue

Which of the following correctly represents the coordinates of the foci of the ellipse shown below?
(x-7)²/4+(y+3)²/16=1

Answers: 1

Show answers

Answers

Answer from: isabellemdeakin

Using the equation of the ellipse, it is found that the coordinates of the foci are:

$(7, -3 - \sqrt{12})$ and $(7, -3 + \sqrt{12})$ .Equation of an ellipse:The equation of a vertical ellipse of center (x_0,y_0)

is given by:

$\frac{(x - x_0)^2}{b^2} + \frac{(y - y_0)^2}{a^2} = 1$

The coordinates of the foci are as follows: $(x_0, y_0 \pm c)$ , in which the coefficient c is given by:

c^2 = a^2 - b^2

In this problem, the equation is:

$\frac{(x - 7)^2}{4} + \frac{(y + 3)^2}{16} = 1$

Hence, x_0 = 7, y_0 = -3, a^2 = 16, b^2 = 4 .

The coefficient c is given by:

c^2 = a^2 - b^2

c^2 = 16 - 4

c^2 = 12

$c = \sqrt{12}$

The, the foci are located at: $(7, -3 - \sqrt{12})$ and $(7, -3 + \sqrt{12})$ .

To learn more about equation of ellipses, you can take a look at link

Answer from: mxxrrr

Step-by-step explanation:

You don't have anything listed to choose from but that's ok, we can find them anyways. An ellipse wraps itself around the foci and is either a horizontal or a vertical ellipse. If it is a horizontal ellipse, the foci will share the same y coordinate as the center; if it is a vertical ellipse, the foci will share the same x coordinate as the center. We need to first determine whether this is a horizontal or a vertical ellipse.

In the equation for an ellipse, whether it is horizontal or vetical, there are a and b values. In an ellipse, the a value is ALWAYS bigger than the b value. Because of this, if the a value is under the x coordinate of the ellipse, then the ellipse is horizontal; if the a value is under the y coordinate of the ellipse, then the ellipse is vertical. Because the larger value of a (a^2 = 16 so a = 4) is under the y coordinate of the ellipse, this is a vertical ellipse and the foci will share the same x coordinate as the center. Let's find the center. Our center is (7, -3).

The formula to find the foci (7, -3+c) and (7, -3-c)

c^2=a^2-b^2 , similar to Pythagorean's theorem. Don't make that mistake. Pythagorean's Theorem is used to find the c value in a hyperbola, not an ellipse. For us,

c^2=16-4 so

$c=\sqrt{12}=2\sqrt{3}$

This means that the foci are located at (7, -3+2√3) and (7, -3-2√3)

Not sure what form you need that in, but the decimal equivalencies are:

(7, .4641016151) and (7, -6.464101615)

Answer from: Quest

Ibelieve the answer would be 7, 13, 23

Answer from: Quest

whaere is the picture

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, mncampbell01

Answer asap ! the shortest path from point a to point b goes through a pond. to avoid the pond, you must walk straight 34 meters along one edge of the pond, then take a 90 degree turn, and again walk straight 41 meters along another edge of the pond to reach point b. about how many meters would be saved if it were possible to walk through the pond? a. 11 m b. 20 m c. 30.45 m d. 21.73 m

Answers: 1

continue

Mathematics, 21.06.2019 18:00, kcameronanderso

Liz is shipping a package to her friend. the maximum weight of a medium flat-rate box is 20 pounds, including the box which weighs 6 ounces. write and solve an inequality to describe the possible weight ,w, of the contents that liz will ship to her friend if she must use a medium flat-rate box.

Answers: 2

continue

Mathematics, 21.06.2019 18:00, jedsgorditas

The los angels ram scored 26, 30, 48, and 31 pts in their last four games. how many pts do they need to score in super bowl liii in order to have an exact mean average of 35 pts over five games. write and solve and equation. use x to represent the 5th game.

Answers: 1

continue

Mathematics, 22.06.2019 04:20, Ahhskii

The weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to ac voltage. the values of the parameters depend on the voltage and temperature; suppose α = 2.5 and β = 190. (a) what is the probability that a specimen's lifetime is at most 250? less than 250? more than 300? (round your answers to four decimal places.) at most 250 less than 250 more than 300 (b) what is the probability that a specimen's lifetime is between 100 and 250? (round your answer to four decimal places.) (c) what value is such that exactly 50% of all specimens have lifetimes exceeding that value? (round your answer to three decimal places.) hr

Answers: 2

continue

You know the right answer?

Which of the following correctly represents the coordinates of the foci of the ellipse shown below?...