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AleksAgata [21]
3 years ago
9

Find the equation of the ellipse with the following properties. The ellipse with foci at (0, 6) and (0, -6); y-intercepts (0, 8)

and (0, -8).
Mathematics
1 answer:
sesenic [268]3 years ago
8 0
Hi, thank you for posting your question here at Brainly.

The general equation of a horizontal ellipse is

(x-h)2/a2 + (y-k)2/b2 = 1, at center (h,k) while a = semi-major axis, b = semi-minor axis. These are related through the distance of the focus from the center,c. a2 = b2 + c2.

If you draw the points on a coordinate plane, the center of the ellipse is at (0,0), so h and k equals 0. Then, the minor axis (2b) spans from 8 to -8 of the y-axis. This is equal to 16 units. Hence,

2b = 16
b = 8
b^2 = 64

The distance between the two foci is 2c. Thus,

2c = 12
c = 6
c^2 = 36

Then, a2 = 64 + 36 = 100. Substituting to the general equation:

x^2/100 + y^2/64 = 1
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3 years ago
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2. The rectangular floor of a garage has an area of 198 square feet. Andy knows that the floor is 7
Charra [1.4K]

Answer:

length = 18 ft

Step-by-step explanation:

Let w = width

L = w+7

Area = l*w

198 = (w+7) (w)

Distribute

198 = w^2 +7w

Subtract 198 from each side

0 = w^2 +7w -198

Factor

What 2 numbers multiply to -198 and add to 7

18* -11 = -198

18+-11 = 7

0=(w+18) (w-11)

Using the zero product property

w+18 =0  w-11=0

w= -18   w=11

We cannot have negative width  so w=11

We want the length

l = w+7

l = 11+7 = 18

6 0
3 years ago
Simplify.<br> (w^2 + 3w)-(w^2+5w-4<br><br> 8w-4<br> 2w^2 +8w-4<br> -2w+4<br> -2w
chubhunter [2.5K]

Answer:

-2w + 4

Step-by-step explanation:

Remove parenthesis because they make life semi-confusing but remember to distribute the negative: w^2 + 3w -w^2 - 5w + 4

Combine like terms: w^2 - w^2 cancel out ; 3w - 5w = -2w ; 4

-2w + 4

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3 years ago
*<br> Write the equation in standard form using integers.<br><br> y=-4/5x+3
svetoff [14.1K]

Answer:

4x + 5 y = 15

Step-by-step explanation:

6 0
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