Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at the foci of the ellipse. How far from the center of the ellipse will the spots be located? A. 2 feet
B. 4 feet - incorrect
C. 3 feet
D. 2.5 feet
E. 3.5 feet

Draw the elliptical gate and show the foci, the width, and height as in the figure below.

Note that

a = 5 ft, the width

b = 3 ft, the height

The center is at (0,0).

The foci are at (c, 0) and at (-c, 0).

The foci are related to a and b by

c² = a² - b²

   = 5² - 3² = 16

c = +4 or -4

The foci are located 4 ft horizontally from the center of the ellipse.

I hope I can help you with your first question!

2.5 feet

Step-by-step explanation:

Im sry if its not right

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

d

step-by-step explanation: