Consider the two points f(−9, 0) and , 0) in the coordinate plane. what is the equation of the
ellipse given as the set of all points p in the coordinate plane satisfying fp + pg = 30? write the
equation in the form
x^2 / a^2 + y^2 / b^2 = 1 with a and b real numbers, and explain how you obtain your
answer.

Step-by-step explanation:

Let's call P(x,y). For F(-9,0) and G(9,0), FP represents the distance between F and P, and PG, the distance between P and G. For an ellipse, F and G are the focus, which is in x ax (y = 0).

The equation is given by:

dFP + dPG = 2a

FP + PG = 30 --> 2a = 30 --> a = 15

The point in the x ax is called c = 9

And the relation between them are:

c² = a² - b²

9² = 15² - b²

b² = 225 - 81

b² = 144

b = √144

b = 12

So, the equation of the ellipse is:

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.