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

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

In this problem, the equation is:

Hence, .

The coefficient c is given by:

The, the foci are located at: and .

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

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)

, 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,

so

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: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft