(a) Sketch the conic section. Find and label any foci, vertices, and asymptotes. (x - 3)^2 – 9y^2 = 36
(b) Find the equation of the ellipse with foci (0,+2) and semi-major axis length 3.
Answers
a) the vertices are (9, 0) and (-3, 0).
the foci are (3 ± 2√10, 0)
the asymptotes are y = ±x/3 - 1
b) the equation of the ellipse is x² + (y-√5/2)² = 5/4
a) To find the foci, vertices, and asymptotes of the ellipse (x - 3)² - 9y² = 36, we can first divide both sides by 36 to get:
[tex]\frac{(x-3)^2}{36} - \frac{y^2}{4}=1[/tex]
Therefore, the center of the ellipse is (3, 0).
The semi-major axis length is √36 = 6, and the semi-minor axis length is √4 = 2.
Therefore, the vertices are (3 ± 6, 0) = (9, 0) and (-3, 0).
The foci are located at a distance of √(6²-2²) = 2√10 from the center along the major axis. Therefore, the foci are (3 ± 2√10, 0) and the equation of the major axis is x = 3.
To find the asymptotes, we will use the formula:
[tex]\frac{y-k}{b} = \pm\frac{x-h}{a}[/tex]
where (h, k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis. Therefore, the equations of the asymptotes are:
(y-0)/2 = ±(x-3)/6
y = ±x/3 - 1
b) To find the equation of the ellipse with foci (0, 2) and semi-major axis length 3, we can first find the center of the ellipse. Since the foci are located on the y-axis, the center must also be located on the y-axis. Therefore, the center is (0, c), where c is the distance between the center and one of the foci.
Since the semi-major axis length is 3, the distance between the center and one of the vertices is 3. Therefore, we have:
c² + (3/2)² = (3/2+2)²
c² = 5/4
Therefore, the center of the ellipse is (0, √5/2). The distance between the center and one of the foci is √5/2 - 2. Therefore, the distance between the center and one of the vertices is √{(√5/2)² - (√5/2 - 2)²} = √5.
Therefore, the semi-minor axis length is √5/2, and the equation of the ellipse is:
[tex]\frac{x^2}{\frac{5}{4} } +\frac{(y-\frac{\sqrt{5}}{2} )^2}{\frac{5}{4} } =1[/tex]
x² + (y-√5/2)² = 5/4
Learn more about Ellipse here
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Answer:
4 4/7
Step-by-step explanation:
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4 4/7
Answer:
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Step-by-step explanation:
4/7 x 8 = 32/7
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Answer:
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Answer:
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Step-by-step explanation:
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Answer:
x^14
Step-by-step explanation:
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opt1.
667/1000
=66.7
hope u understand
Answer:
more like dividing the up ones with bottom ones
EX 717/1000=0.717
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circumference:
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Answers
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Answer:
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Step-by-step explanation:
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Well, the correct fraction would be 2 and 2/5 because this is what the model shows.
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Answers
Step-by-step explanation:
i hope you will get the answer
Step-by-step explanation:
2x - 5 ( 4 + 3 ( x + 2 ) ) = 92x - 5 ( 4 + 3x + 6 ) = 92x - 5 ( 3x + 10 ) = 92x - 15x - 50 = 9-13x - 50 = 9-50 - 9 = 13x-59/13 = xMARK ME AS BRAINLIST#every one when im in public be like
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
22
Step-by-step explanation:
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Answer:
22
Step-by-step explanation:
4a + b2
4(4) + (3)2
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Answer:
11
Step-by-step explanation:
Work backwards and reverse the operations to find the original number.
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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True
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Answer:
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Step-by-step explanation:
.................,,,,,,,,,,,................
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Answers
9514 1404 393
Answer:
y = 21
Step-by-step explanation:
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Answer:
<2, <3, <4
Step-by-step explanation:
You have parallel lines cut by a transversal, so alternate interior angles are congruent. Also, alternate exterior angles are congruent. Corresponding angles are congruent.
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Answers
Answer:
x = -40 and y = -64
Step-by-step explanation:
The ratio of the two numbers is 5/8, since the difference of these two numbers is 24, what is the sum
Let two numbers be x and y.
ATQ,
x-y = 24 ..(1)
and
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or
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Subtract equation (3) from (2).
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x+64 = 24
x = -64+24
x = -40
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Answers
Answer:
9-(-15)
Step-by-step explanation:
because it would be changed to 9+15
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Answers
Answer:
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Step-by-step explanation:
Mori is building a cage for his pet guinea pig. The bottom is 8 inches
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Answers
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//
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Answer:
185
Step-by-step explanation:
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Answer:
3.91421356237
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Step-by-step explanation:
Find the measure of the indicated angle to the nearest degree
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Answer:
61.92°
Step-by-step explanation:
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Answers
Answer:
68°
Step-by-step explanation:
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Answers
Answer:
Mean = 3.5
Median = 3.5
Mode = 5, 2
Step-by-step explanation:
Hope that helps!
Mean: To find the mean, simply add the numbers together and divide by the amount of numbers in the set:
Mean: (5 + 2 + 5 + 2)/4
= (14)/4
= 3.5
Mean = 3.5
Median: To find the median, simply order from least to greatest, and find the middle number in the set. That is your median. In the case of an even amount of numbers in the set, find the mean with the two median numbers (as in this case):
Median: (2 + 5)/2
= 7/2
= 3.5
Median: 3.5
Mode: The Mode is the number that shows up the most frequently. As both given numbers show up the same amount of times (twice), there is no mode.
Mode: None.
Range: The Range is found by subtracting the greatest number with the least number:
5 - 2 = 3
Range: 3
How might a change in the environment affect plants differently than it would animals?
Answers
Answer:
Some plants need certain things in their environment, so if their environment changes it could make the plants not grow. Animals would most likely either move to a different area or would get used to the change.