ellipse with vertices (-3, 4), (11, 4) and foci (-1, 4), (9.4)?
Answers
Answer:
[tex]\frac{(x-4)^2}{49}+\frac{(y-4)^2}{24}=1[/tex]
Step-by-step explanation:
Because the vertices are on the same horizontal line and so are our foci, this is our major axis for a horizontal ellipse.
Horizontal Ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
a>b
Major axis length: 2a
Minor axis length: 2b
Center: (h,k)
Foci: (h±c,k) where a²-b²=c²
We can easily find the center of the ellipse by finding the midpoint of our vertices (-3,4) and (11,4) which works out to be (4,4)
Because our foci must be (-1,4) and (9,4) this means (4±c,4) represents our foci. We can easily see that c=5 since (4-5,4) -> (-1,4) and (4+5,4) -> (9,4).
Knowing that c=5, we need to determine our values for a and b to satisfy the equation a²-b²=5². Our vertices are located on the major axis, which will help us in finding the value of a. The distance between the two vertices will be the length of the major axis, which will be |11-(-3)| = 14. Additionally, because the length of the major axis is equal to 2a, this means 2a=14 where a=7. Now we can solve for b with our equation 7²-b²=5² where b=√24.
In conclusion, our ellipse would be:
[tex]\frac{(x-4)^2}{7^2}+\frac{(y-4)^2}{\sqrt{24}^2}=1[/tex] which works out to be [tex]\frac{(x-4)^2}{49}+\frac{(y-4)^2}{24}=1[/tex]
The equation of ellipse with vertices (-3, 4), (11, 4) and foci (-1, 4), (9.4) is
(x-4)^2/49 + (y-4)^2/24 = 1
What is equation of an ellipse?The standard equation of an ellipse centered at (h, k) with a major axis parallel to the x-axis is given by:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where the coordinates of the vertex are (h±a, 0), coordinates of co-vertex are (h, k ± b) and the coordinates of foci are (h±c, k), where a² = c² + b².
here, we have,
Because the vertices are on the same horizontal line and so are our foci, this is our major axis for a horizontal ellipse.
Horizontal Ellipse:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where,
a>b
Major axis length: 2a
Minor axis length: 2b
Center: (h,k)
Foci: (h±c,k) where a²-b²=c²
We can easily find the center of the ellipse by finding the midpoint of our vertices (-3,4) and (11,4) which works out to be (4,4)
Because our foci must be (-1,4) and (9,4) this means (4±c,4) represents our foci. We can easily see that c=5 since (4-5,4) -> (-1,4) and (4+5,4) -> (9,4).
Knowing that c=5, we need to determine our values for a and b to satisfy the equation a²-b²=5².
Our vertices are located on the major axis, which will help us in finding the value of a.
The distance between the two vertices will be the length of the major axis, which will be |11-(-3)| = 14.
Additionally, because the length of the major axis is equal to 2a, this means 2a=14 where a=7.
Now we can solve for b with our equation 7²-b²=5² where b=√24.
In conclusion, our ellipse would be:
(x-4)^2/49 + (y-4)^2/24 = 1
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Related Questions
Sage and Tom started the month with the same number of talk minutes on their cell phones. Sage talked for 7 minutes with her dad. Tom talked for 4 minutes with a friend and 3 more minutes with his mom. Do Sage and Tom have the same number of talk minutes left on their cell phone plans?
Complete the model to represent Sage’s minutes.
Enter the correct answers in the boxes.
Answers
Answer
omgggggggg same i dont know how to do it either
Step-by-step explanation:
Answer:
there is 11 min all to together for sage and tom so they did not have the same cell phone line
Step-by-step explanation:
its easy
In two or more complete sentences, describe the similarities and differences of making a purchase with a debit card and/or a credit card.
Answers
Answer:
See below
Step-by-step explanation:
When you make purchases with a debit card, you are borrowing funds from your own bank account. When you make purchases with a credit card, you are borrowing funds from the bank, typically to pay it back to the bank later.
What percent of the data is less than 10 texts?
Group of answer choices
25%
50%
75%
100%
Answers
Please help me with this math problem!!!
Answers
Answer:
A) 840 Miles
B) 14 Milers per Gallon
Step-by-step explanation:
A) 350/24 = 14 miles per gallon
14 X 60 = 840 miles.
B) 350/24 = 14 miles per gallon
In the triangle below, what is the length of EF
A. 6
B. 24
C. 12
D. 25
Answers
Answer:
12
Step-by-step explanation:
since DE and EF are congruent then we now know that EF is also 12
A rectangular pasture has a fence around the perimeter. The length of the fence is 8x^7 and the width is 6x^4. What is the area of the pasture?
Answers
Answer:
Answer:
The area of the rectangular pasture is 768x^{11}\ unit^{2}.768x
11
unit
2
.
Step-by-step explanation:
Formula
Area of a rectangle = Length × Breadth
As given
A rectangular pasture has a fence around the perimeter. The length of the fence is 16x^{7}16x
7
and the width is 48x^{4}48x
4
.
Put all the values in the formula
Area\ of\ a\ rectangular\ pasture = 16x^{7}\times 48x^{4}Area of a rectangular pasture=16x
7
×48x
4
Now by using the exponent
x^{a}\times x^{b} = x^{a+b}x
a
×x
b
=x
a+b
Area\ of\ a\ rectangular\ pasture = 16\times 48\times (x^{7+4})Area of a rectangular pasture=16×48×(x
7+4
)
Area\ of\ a\ rectangular\ pasture = 768(x^{11})Area of a rectangular pasture=768(x
11
)
Therefore the area of the rectangular pasture is 768x^{11}\ unit^{2}.768x
11
unit
2
.
Answer:
C. 768x11
Step-by-step explanation:
(find the value of x from the given
figures.)
F
a)
120
3
solo
Answers
Answer:
sorry,
can u repost yr question with figure plz
stay safe healthy and happy.Mary invested $15,000 in an account that paid 5% simple interest annually. She will not
make any additional deposits or withdrawals. How much interest will Mary earn on her
investment at the end of 3 years?
$2,250.00
F
$17,364.38
H
$50,625.00
J
$225,000.00
Answers
Answer:
$2,250
Step-by-step explanation:
5% of 15,000 is 750. If we multiply 750 by the number of terms, 3, we get an answer of $2,250.
Answer:
$2,250
Step-by-step explanation:
Use the simple interest formula i = prt. Here the principal, p, is $15,000 and the interest rate, r, is 0.05. Then:
i = ($15,000)(0.05)(3) = $2,250
Bobby is playing hide-and-seek with Clarence and Heather. Clarence is hiding 75 feet south of
Bobby, and Heather is hiding due east of Clarence. If Bobby is 85 feet from Heather, how far
apart are Clarence and Heather?
Answers
Which function BEST expresses the linear relationship displayed by the scatter plot?
A)
y = 0.25x + 1
B)
y = 0.25x + 3.75
C)
y = 0.25x + 8.25
D)
y = 0.50x + 3.75
Answers
Answer:
0.25x + 1cu a linear equation has one as it highest and lowest power of it variable
If you work 11 hours per week and get paid 11.71 per hour how much do you get paid per month and per year
Answers
515 per month
6182 per year
Please someone help me I don’t understand please please help
Answers
Answer:
604
Step-by-step explanation:
Answer:
604
Step-by-step explanation:
6x10^2+4
6x100+4
600+4
= 604
WILL GIVE BRANLEST EXPLAIN
Solve for x:
Answers
Answer:
Angle between two tangents or two secants is the half of the difference of intercepted arcs.
#1
x = 1/2(250° - (360° - 250°)) = 1/2(250° - 110°) = 1/2(140°) = 70°#2
50° = 1/2(170° - x)100° = 170° - xx = 170° - 100°x = 70°A female sea turtle buries 200 eggs in the sand. After the baby turtles hatch they hurry to make it to the relative safety of the ocean. Of the 176 babies that hatched, 124 were eaten by birds, 37 were eaten by other predators, and 3 ran the wrong direction. Suppose that just after the eggs were laid that you marked one with an X. What is the probability that your egg hatched and the baby turtle made it to the ocean?
Answers
Answer: 12%
explanation: i subtracted the ones that had been eaten, and the ones that ran off and solved for x.
CAN SOMEONE HELP ME PLSS IM FAILING AND I RLLY NEED HELP HELP ASAP HELP MATH MATH MATH HELPPPPPPPPPP
Answers
Answer:
Hello if I know the answers to your math questions I'll answer if there already posted I'll check your profile if not please post them thank you!
7 1/2 divided by (4 1/2 - 5 1/8) =
Answers
Answer:
−12 if simplfied .
Step-by-step explanation:
A ladder which is 6.7 m long is placed on the ground 2.8 m from a vertical wall and then leaned over to the wall. How high up the wall can the ladder reach? Give your answer rounded to 1 DP.
Answers
Answer:
6.1 m
Step-by-step explanation:
Always draw a diagram! And now pythagorean theorem. a^2 + b^2 = c^2
Substitution:
a^2 + 2.8^2 = 6.7^2
a^2 + 7.84 = 44.89
a^2 = 37.05
a = 6.086...
Rounding up to one decimal point, thats 6.1 m
What is the answer for 2v-6/3-v ?
Answers
Step by step explanation:
2v−6
3-v
Factor the expressions that are not already factored.
2(v−3)
−v+3
Extract the negative sign in −3+v.
−2(−v+3)
−v+3
Cancel out −v+3 in both numerator and denominator.
−2
Answer:
-2
8 1/4 x 4 1/2 x 6 1/2
Answers
Answer:
[tex]241\frac{5}{16}[/tex]
Step-by-step explanation:
Mark as Brainliest
Answer:
[tex]214\frac{5}{16}[/tex]
Step-by-step explanation:
Estimate: 55 +8
50
60
7
8
Answers
Answer:
60But the actual solution is 63.
Step-by-step explanation:
55+8=63
63
3<5 so you don't round up, you round down.
Rounding down... 60
60
But the actual solution is 63.
Find the distance d. Round your answer to the nearest tenth. Show all your work. Thanksss!
Answers
Answer: the distance for d is about 5.8 units
Step-by-step explanation:
Use the pythagorean theorem. a^2 + b^2+= c^2 . in this case, c^2 is the distance for d.
5^2 + 3^2= d^2
25+9= d^2
34= d^2
square both sides and d is approximately 5.818
If the measurement of angle 2 is 120 degrees, what is the measurement of angle 7?
Answers
Answer:
The measure of angle 7 is twice the measure of angle 2, then the measure of angle 7 is
angles 2 and 7 equal 180 degrees. 180 = 2x + x
180 = 3x
x = 60
angle 7 is twice x
angle 7 = 120
Step-by-step explanation:
What is the common ratio of the geometric sequence below? 18, -6, 2, -2/3
Answers
Answer:
Step-by-step explanation:
Common ratios are found by either multiplying the same number in to get to the next number in the sequence, or by dividing out the same number in to go the next number in the sequence. Multiply or divide, NOT add or subtract! Be careful! Obiviously, our numbers are going down, so we are dividing out a specific number as opposed to multiplying one in. To get from 18 to 6, we have to divide by 3; however, the 6 is negative, so we have to divide by -3. To determine if we are correct, divide -6 by -3 and see if that result is the next one in line. -6 divided by -3 is 2. So we are correct, and the common ratio is -3.
What is the radius and center of a circle with the equation (x – 2)2 + (y – 3)2 = 36?
radius: 6 units; center: (2, 3)
radius: 36 units; center: (2, 3)
radius: 6 units; center: (–2, –3)
radius: 36 units; center: (–2, –3)
Answers
Answer:
A
Step-by-step explanation:
Commenter is right cause I graphed it to doublecheck
The centre and radius of the circle is (2, 3) and 6 units respectively
What are equation of a circle?The standard equation of a circle is expressed as:
(x – a)² + (y – b)² = r²
where:
centre = (a, b)r is the radiusGiven the equation
(x – 2)² + (y – 3)² = 36
Compare
(a, b) = (2, 3)
r² = 36
r = 6 units
Hence the centre and radius of the circle is (2, 3) and 6 units respectively
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Algebra 1
-15 points-
Solve the following
absolute value equation.
-10|5x + 5| = 100
Answers
Answer:
no solution
Step-by-step explanation:
The absolute value function always gives a positive value, that is
| - a | = | a | = a
Given
- 10 | 5x + 5 | = 100 ( divide both sides by - 10 )
| 5x + 5 | = - 10
The absolute value cannot be negative thus the equation has no solution
y is directly proportional to the square root of x
if y = 60 when x = 36
find x when y = 80
Answers
80 = x^2
x = √80
x = 8.94
Answer:
x = 64
Step-by-step explanation:
Given y is directly proportional to [tex]\sqrt{x}[/tex] then the equation relating them is
y = k[tex]\sqrt{x}[/tex] ← k is the constant of proportion
To find k use the condition y = 60 when x = 36, then
60 = k [tex]\sqrt{36}[/tex] = 6k ( divide both sides by 6 )
10 = k
y = 10[tex]\sqrt{x}[/tex] ← equation of proportion
When y = 80 , then
80 = 10[tex]\sqrt{x}[/tex] ( divide both sides by 10 )
8 = [tex]\sqrt{x}[/tex] ( square both sides )
64 = x
ANSWER BOTH!!! A. An international company has 18,600 employees in one country. If this represents 18.2% of the company's employees, how many employees does it have in total?
Round your answer to the nearest whole number.
B. A house on the market was valued at $316,000. After several years, the value decreased by 7%. By how much did the house's value decrease in dollars? What is the current value of the house?
Decrease in value: $
Current house value:$
Answers
Answer:
A. 102,198 employees
B. $22,120 decrease
$293,880 current value
Step-by-step explanation:
Please show full solutions! Will mark brainliest for the best answers! Thanks. Question is attached.
Answers
9514 1404 393
Answer:
a square 175 m on a side
Step-by-step explanation:
Let x and y represent the sides of the rectangle. Then the perimeter is ...
P = 2(x + y) = 700
x + y = 350 . . . . . . . divide by 2
y = 350 -x . . . . . . . . subtract x
The area of the fenced field is ...
A = xy
A = x(350 -x)
This is a quadratic function that has zeros at x = 0 and x = 350. The axis of symmetry is x = (0 +350)/2 = 175. The vertex (maximum area) is on the axis of symmetry, so corresponds to x = 175. The y-value there is ...
y = 350 -x = 350 -175 = 175
That is, the maximum area will be obtained when the fenced area is a square. Each side of the square is 175 m, which is 1/4 of the total length of the fence.
The dimensions of the space are 175 m by 175 m.
A student has taken three math tests so far this semester. His scores for the first three tests were 71, 75, and 79. Part A: Suppose his test scores continue to improve at the same rate. What will be the grade on the sixth and (final) test?
Answers
Answer:
The grade of this sixth and (final) test would be 91.
Step-by-step explanation:
This is an arithmetic series since each time the data is increasing by the common difference of 4, and we already know a₁ which is the first term in the sequence is 71, therefore we can say:
a₁ = 71
r = 4
a₆ = the sixth term that needs to be found out
n = 6
Formula of an arithemetic series:
aₙ = a₁ + r(n - 1)
a₆ = 71 + 4(6 - 1)
a₆ = 71 + 4(5)
a₆ = 71 + 20
a₆ = 91
Hence, the grade of this sixth and (final) test would be 91.
Hope this helps!
Ann and ben had some apples. The ratio of the number of Ann's apples to the ratio of Ben's apple is 2:3. Ann gave 6 apples to ben and now the ratio becomes 1:3. How many apples are all together?
Answers
Answer:
There are 12 apples in total.
Step-by-step explanation:
If Anne gave Ben 6 apples then heres how:
2:3 subrtact 6 apples = 1:3
6 apples x 2 = 12 apples =
2 ÷ 2 = 1
Hence, your answer is double 6 which is 12 apples.
Hope this helps :)