Part 3: Write the equation of and graph an ellipse.
Given the foci and vertices of an ellipse, complete the following steps.
Vertices at (4, -6 +-9)
Foci at (4, -6 +-5sqrt2)
a) What is the center of the ellipse? Explain how to determine this from the given points.
b) Write the standard equation of the ellipse. (3 points
c) What are the lengths of the major and minor axes? (2 points)
Major Axis:
Minor Axis:
d) Sketch a graph of the ellipse and label the center, foci, and the major and minor axes. (4 points)
Answers
Answer:
Step-by-step explanation:
The center is halfway between vertices, at (4, -6).
It is also halfway between foci.
:::::
The vertices are vertically aligned, so the parabola is vertical.
General equation for a vertical ellipse:
(y-k)²/a² + (x-h)²/b² = 1
with
center (h,k)
vertices (h,k±a)
co-vertices (h±b,k)
foci (h,k±c), c² = a²-b²
Apply your data and solve for h, k, a, and b.
center (h,k) = (4, -6)
h = 4
k = -6
vertices (4,-6±a) = (4,-6±9)
a = 9
foci (4,-6±c) = (4,-6±5√2)
b² = a² - c² = 9² - (5√2)² = 31
b = √31
The equation becomes
(y+6)²/81 + (x-4)²/31 = 1
:::::
length of major axis = 2a = 18
length of minor axis = 2b = 2√31
The various parts of the question needs to be answered.
Center: (4,-6)
Standard equation: [tex]\dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis: 18 units
Length of minor axis: [tex]2\sqrt{31}\ \text{units}[/tex]
Graph is attached.
EllipseThe Vertices are of the form
[tex](h,k\pm a)=(4,-6\pm 9)[/tex]
This means that the ellipse is symmetrical to the y axis.
The center of an ellipse is given by [tex](h,k)[/tex]
So, here the center is [tex](4,-6)[/tex]
[tex]a=\pm 9[/tex]
The foci are of the form
[tex](h,k\pm c)=(4,-6\pm 5\sqrt{2})[/tex]
So, [tex]c=\pm 5\sqrt{2}[/tex]
[tex]b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{9^2-(5\sqrt{2})^2}\\\Rightarrow b=\pm\sqrt{31}[/tex]
The standard equation for major axis being parallel to y axis is given by
[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis is
[tex]2a=2\times 9\\ =18\ \text{units}[/tex]
Length of minor axis is
[tex]2b=2\sqrt{31}\ \text{units}[/tex]
Learn more about ellipse:
https://brainly.com/question/12205108
Related Questions
Answer these correctly I’ll give brainalist + 10 points
Answers
A certain town never has two sunny days in a row. Each day is classified as being either sunny, cloudy (but dry), or rainy. If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is 60% of chance that it will be the same the next day, and if it changes then it is equally likely to be either of the other two possibilities. In the long run, how frequent are we observing a day for which it is rainy and the next two days are also rainy
Answers
Answer:
In the long run if one day is rainy there is frequency of 2/5 that other two days will also be rainy.
Step-by-step explanation:
A matrix is formed to classify the weather conditions. It is given that if one day is sunny then there is likely chance that the next day will be cloudy, but if one day is rainy then there is 60% chance that next day will be same. To identify the possibility of next two days we create probability matrix;
Probability (P) = [tex]\left[\begin{array}{ccc}0&\frac{1}{2} &\frac{1}{2} \\\frac{1}{4} &\frac{1}{2} &\frac{1}{4} \\\frac{1}{4} &\frac{1}{4} &\frac{1}{2} \end{array}\right][/tex]
After solving for probability we get a fraction of 2/5
Select all the expressions that could represent the volume of a box, which is a third degree polynomial in variables x and y.
A. 3 x y − 3 x y^2
B 2y-xy^3+7
C.3x^3y^2-3x^2y+10y^2-10y
D. 3x^2y+5xy
E. 3y^3+3x^3y^4
Answers
Answer:
A and D
Step-by-step explanation:
Third degree polynomials refers to polynomials that has 3 as the greatest power of the variable.
A. 3 x y − 3 x y^2
Degree = 1 + 2 = 3
This option is correct
B 2y - xy^3 + 7
Degree = 1 + 3 = 4
This option is wrong
C. 3x^3y^2 -3x^2y + 10y^2 - 10y
Degree = 3 + 2 = 5
This option is wrong
D. 3x^2y+5xy
Degree = 2 + 1 = 3
This option is correct
E. 3y^3 + 3x^3 y^4
Degree = 3 + 4 = 7
This option is wrong
Factor completely 185-32 Enter your answer in the boxes
Answers
Answer:
2 (9b - 16)
Step-by-step explanation:
18b - 32
2 (9b - 16)
Answer:
2(9b-16)
Step-by-step explanation: I looked it up on m a t h w a y sorry if its wrong! <3
Sharon is using a calculator to find out how many hours she has spent on a certain job.She divides,and her display reads:
Answers
what does it read????
i want to answer the question but i dont have any information
I just need help cause if I don’t I don’t know what imma do
Answers
Answer:
[tex]P(32) = \frac{1}{90}[/tex]
[tex]P(Odd) = \frac{1}{2}[/tex]
[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]
Step-by-step explanation:
Given
Sample Space = 10 to 99
First, we calculate the sample size (n)
[tex]n = 99 - 10 + 1[/tex]
[tex]n = 90[/tex]
Solving (a): P(32)
In 10 to 99, there is only 1 32.
So,
[tex]P(32) = \frac{n(32)}{n}[/tex]
[tex]P(32) = \frac{1}{90}[/tex]
Solving (b): P(Odd)
There are 45 odd numbers between 10 and 99
i.e.
[tex]n(Odd) = 45[/tex]
So:
[tex]P(Odd) = \frac{n(Odd)}{n}[/tex]
[tex]P(Odd) = \frac{45}{90}[/tex]
[tex]P(Odd) = \frac{1}{2}[/tex]
Solving (c): P(Multiple of 5)
There are 18 multiples of 5 between 10 and 99
i.e
[tex]P(Multiples\ 5) = \frac{18}{90}[/tex]
[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]
Helpppppppppppppppppppppppppppppppp
Answers
Answer:
2/9 in the simplist form
Step-by-step explanation:
you multiply both the fractions for the area
then simplify
What is the equation of the line in the slope intercept form?
Answers
Answer:
y = mx+b is the equation for slope-intercept form
Step-by-step explanation:
m=slope
x=independent variable
y= y-intercept
Answer:
y=-2x
Step-by-step explanation:
Miguel ran 15 yards. What distance is that in feet? HELPPPP
Answers
Answer: 45 feet 1 yard= 3 feet so 3 feet times 15 is 45 feet
Step-by-step explanation:
Answer:
45 ft
Step-by-step explanation:
1 yd = 3 ft
15 yd = 3(15) ft
15 yd = 45 ft
What is the answer? A, B, C, or D
Answers
please help i'm really stuck
Answers
how will apply the lesson i have learned in real life scenari
ill so you the picture of it
Answers
Answer:
Of WhaT?
Thanks for the free points btw
ASAP BRAINLY I WON'T GET FULL GRADE IF ITS MISSING!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1. Trapezoid.
2. Rectangle, Parallelogram
3. Rhombus, Parallelogram
4. Rectangle, Parallelogram, Square
5. No, a figure cannot have more than one parallel side and exactly one parallel side at once.
Step-by-step explanation:
Hope ths helped.
What is the answer?
A)44
B)42
C)45
D)48
Answers
Answer:
44
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
because you take 3 pulse 2
−2 2/21 +(−0.25÷(− 1/4 )−1.5÷(− 3/16 ))÷(−4 1/11 )
pls answer this is a hundred point question
Answers
The answer is -4.29523809524 . (The second period is NOT another point. It’s just marking the end of a sentence. Yes, I’m a grammar & math freak)
Answer:
-4.29523809524
Step-by-step explanation:
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Answer:
angle 3 is 132
angle 2 is 48
Step-by-step explanation:
17 × 5/8 mixed solution
Answers
Answer:
10 5/8
Step-by-step explanation:
17/1 x 5/8. Multiply numerators together and denominators you will get 85/8. Then you convert the improper fraction.
Answer:
10 5/8
Step-by-step explanation:
17 × 5/8 = 85/8
Simplify, sub-step b: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
85 ÷ 8 = 10 remainder 5
85/8 = 10 5/8
What’s the answer to this
Answers
Regina read his novel three nights in a row. Each night, he read for 3/4 of an hour. How many hours did regina read his novel altogether?
Answers
Answer:
Regina read for 2 1/4 hours or 2 hours and 15 minutes
Step-by-step explanation:
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what is the slope of the line?
Answers
Slope is 4 over 5
What is the area of this figure?
Question 10 options:
124 in2
112 in2
184 in2
Answers
Answer:
112 in2
Step-by-step explanation:
6 x 4 / 2 + 10 x 10 = 24 / 2 + 100
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Hope that helps!
students recorded the total number of pages and chapters in each of several books on the scatterplot. Based on the sbcatterplot, which is the best prediction of the number of chapters in a book with 200 pages
Answers
Answer:
7
Step-by-step explanation:
Answer: 7
Step-by-step explanation:
heyy i need help on me hw
Answers
Answer:
the answer is b
Step-by-step explanation:
brainliest pleasee?
The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per
year. Which function shows the company's profit as a function of time in years?
a. f(t) = 100,000 0.012^t
b. f(t) = 100,000(1 + 1.2)^t
c. f(t) = 100,000(1 + 0.012)^t
d. f(t) = 100,000 - 1.2^t
Answers
Given:
Initial profit = $100,000
Increasing rate of profit = 1.2%
To find:
The function that shows the company's profit as a function of time in years.
Solution:
The exponential growth model is defined as:
[tex]f(t)=a(1+r)^t[/tex]
Where, a is the initial value, b is the growth rate and t is the time period.
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[tex]f(t)=100,000(1+0.012)^t[/tex]
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Answers
Answer:
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Step-by-step explanation:
I used an online calculator (calculator soup)
Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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and 12 boys in a class.
What would be the probability of
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Answers
Answer:
0.625
Step-by-step explanation:
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20/32=0.625
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Answers
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Answers
Answer:
18/20 chance
Step-by-step explanation:
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Answer:
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Step-by-step explanation: