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

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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

The distance from point a to point c across the coordinate plane is aproxamatly 8.94 rounded to the nearest hundredth. you use a^2 + b^2 =c^2
Apply the pythagorean theorem to find the distance between points a and c