why and how ellipse can help solve real life problems
1. why and how ellipse can help solve real life problems
Answer:
Many real-world situations can be represented by ellipses, including orbits of planets, satellites, moons and comets, and shapes of boat keels, rudders, and some airplane wings. A medical device called a lithotripter uses elliptical reflectors to break up kidney stones by generating sound waves. Some buildings, called whispering chambers, are designed with elliptical domes so that a person whispering at one focus can easily be heard by someone standing at the other focus. This occurs because of the acoustic properties of an ellipse. When a sound wave originates at one focus of a whispering chamber, the sound wave will be reflected off the elliptical dome and back to the other focus. In the whisper chamber at the Museum of Science and Industry in Chicago, two people standing at the foci—about 43 feet apart—can hear each other whisper.
2. what is an ellipse?the major axis of an ellipse is?in an ellipse the foci are?
Answer:
ellipse is a shape that resembles a flattened circle
3. 1. the ellipse is formed by ____________________2. the parts of an ellipse are___________________3. the standard equation of an ellipse are___________________________4. The concepts of ellipse can be useful in the field of___________________________5. I realize that________________________
Answer:
thanks for sharing your experience
Answer:
1.An ellipse is formed by a plane intersecting a cone at an angle to its base
2. center, major axis, minor axis, and foci
3.The equation of an ellipse written in the form (x−h)2a2+(y−k)2b2=1.
4.Ellipses are common in physics, astronomy and engineering.
5. in your own opinion yan b it ch.
4. 1. What is the coordinate of the center of the ellipse? 2. Find the coordinates of the foci of the ellipse. 3. Give the coordinates of the two vertices of the ellipse. 4. The covertices of the ellipse is found in what coordinates? 5. If l and m are segments between the foci and a certain point in the ellipse, how long is l and m combined?
Answer:
1. (0,0)
2. (0, ± 4)
3. (0, ± 5)
4.(0, ±3)
Step-by-step explanation:
1.) (h,k) since it's in the origin, it's (0,0) coordinates
2.) foci is along the major axis, so it's (0 ± 4)
3.) is also along the major axis but it's the outer line of the ellipse
4.) co-ver, is along the minor axis
5. The major axis of an ellipse is the segment with length 2b, perpendicular to the minor axis and whose midpoint is the center of the ellipse. The major axis of an ellipse is the segment with length 2b, perpendicular to the minor axis and whose midpoint is the center of the ellipse. True False.
True if it’s not the correct answer change it
6. the perimeter of a circle or ellipse
Answer:
Comparing. * Exact: When a=b, the ellipse is a circle, and the perimeter is 2πa (62.832... in our example).
– i hope this helps <3
7. what is an ellipse?
Answer:
An ellipse is created by a plane intersecting a cone at the angle of its base. It is shaped like an oval.
Step-by-step explanation:
makatulong po sana.
8. Which of the following is a horizontal ellipse?A. Ellipse with foci (0,3) and (0,-3)B. Ellipse with vertices (4, 4) and (4, -4)C. Ellipse with covertices (5,7) and (11,7)D. Ellipse with focus (-6,-2), covertix (-1, 5) and with horizontal majoraxis
Answer:
Letter: C...............
The answer will be C.
To be more precise:
if x is the same, it is vertical; andif y is the constant, it represents a horizontal ellipse.9. if the foci of an ellipse are very close together the ellipse would look a lot like a a. circleb. ellipsec. hyperbolad. parabola
I think the answer would be B. ellipse
10. what is the symbol for ellipses?
Answer:
ung 3 dots (...) sa huli
Answer:
dot-dot-dot
Step-by-step explanation:
The ellipsis ..., . . ., or (in Unicode) …, also known informally as dot-dot-dot, is a series of (usually three) dots that indicates an intentional omission of a word, sentence, or whole section from a text without altering its original meaning.
11. The midpoint of both axes (major & minor) is the center of Ellipse. What is the eccentricity of an ellipse if a = 5 and b = 3?
Answer:
0.8
Step-by-step explanation:
e = c/a
c² = a² - b²
c² = 5² - 3²
c² = 25 - 9
c² = 16
c = 4
e = 4/5
e = 0.8
12. As you consider the shape of the graph of an ellipse where a = b, can you consider a circle as an ellipse? Why or why not?
Answer:
Yes, because if a is equal to b where as a and b are the length of minor and major axis then an ellipse is considered a circle whose points are equidistant.
13. the foci of an ellipse are at
Answer:
meron na po kaseng answer
Step-by-step explanation:
sorry
14. halimbawa nang ellipse
Answer:
Many real-world situations can be represented by ellipses, including orbits of planets, satellites, moons and comets, and shapes of boat keels, rudders, and some airplane wings. A medical device called a lithotripter uses elliptical reflectors to break up kidney stones by generating sound waves.
Narito ang mga pagkakataon na ginagamitan ng ellipsis
1. Pagtanggal ng salita o pangungusap sa isang pahayag.
2. Pause o pagtigil sa pagsasalita.
3. Hindi tapos na kaisipan ng pangungusap.
4. Pagpapahayag ng hindi katiyakan o uncertainty sa isang pangungusap.
15. the ellipses indicate that a sequence is
Step-by-step explanation:
if a sequence has an ellipsis, it is an infinite sequence. It has an indefinite number of terms
16. which of these defines an ellipse?
Answer:
saan po?
:)))))))))))((((((((((((:
noun Geometry.
a plane curve such that the sums of the distance
17. is a circle an ellipse
Answer:
In fact a Circle is an Ellipse, where both foci are at the same point (the center). In other words, a circle is a "special case" of an ellipse.
18. Find the equation of the ellipse with center at (0,0), vertices at (2,0) and (-2,0), and eccentricity of 2/7. Sketch the ellipse.
Answer:
—The equation of an ellipse with center at (0,0), vertices at (2,0) and (-2,0), and eccentricity of 2/7 is given by the following general equation:
(x^2)/(a^2) + (y^2)/(b^2) = 1
where a and b are the lengths of the semi-major and semi-minor axes, respectively. The distance between the center and the vertices is equal to the length of the semi-major axis, which is 2. The formula for the eccentricity of an ellipse is given by e = √(1 - (b^2/a^2)), therefore a = 2 and b = (2/7)a, b = 2(2/7) = 4/7
so the equation of the ellipse is:
(x^2)/4 + (y^2)/(4/49) = 1
Sketch of the ellipse is a oval shape where the center is at (0,0) and it stretches out more horizontally than vertically, with the distance between the center and the vertices is equal to the length of the semi-major axis, which is 2.
19. what are the foci of the ellipse?
Answer:
LUNAR ECLIPSE:
Earth is passing between moon and sun.
SOLAR ECLIPSE:
moon passes between earth and the sun.
Step-by-step explanation:
types of eclipse:
1.partial-partially covered
2.total-totally covered
3.annular
20. true or false ______ 19. The length of the latus rectum is b2 over a. ______ 20. The two fixed points of the ellipse are c units away from the center of the ellipse. ______ 21. If the minor axis is x = 0, then it is a vertical ellipse. ______ 22. If the vertices of the ellipse are on the x-axis, then it is a vertical ellipse. ______ 23. If the covertices of the ellipse are on the y-axis, then it is a horizontal ellipse. ______ 24. An ellipse has only one focus. ______ 25. Astrology is the branch of science which studies elliptical concepts of how planets move on their orbits.
Answer:
19. True
20.false
21.true
22True
23.false
24.true
25.false
21. what is the Center of an ellipse
Answer:
The center of an ellipse is the midpoint of both the major and minor axes. The axes are perpendicular at the center. The foci always lie on the major axis, and the sum of the distances from the foci to any point on the ellipse (the constant sum) is greater than the distance between the foci.
Answer:
The center of an ellipse is the midpoint of both the major and minor axes. The axes are perpendicular at the center. The foci always lie on the major axis, and the sum of the distances from the foci to any point on the ellipse (the constant sum) is greater than the distance between the foci.
The standard form of the equation for an ellipse is (x−h)2a2+(y−k)2b2=1 ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 , where (h,k) is the center point coordinate, 2a is the length of the major/ minor axis, and 2b is the minor/major axis length..
22. Find the standard equation of an ellipse with foci (-7,6) and (-1,6), the sum of the distances for any point in the foci is 14. with illustration and solution of the problem please kailangan ko talaga.
Answer:
[tex]\mathsf{\dfrac{(x+4)^2}{49}+\dfrac{(y-6)^2}{40}=1}[/tex]
Step-by-step explanation:
SOLUTION:
Since the foci of the ellipse have the same y-coordinate (which is 6), the standard equation of the ellipse is:
[tex]\mathsf{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
(h, k) = location of the center of the ellipse
a = semi-major axis
b = semi-minor axis
[tex]\\[/tex]
The center of the ellipse is located at the midpoint of the two foci. To solve for the location of the center, we can use the midpoint formula.
Midpoint formula:
[tex]\mathsf{x_m=\dfrac{x_1+x_2}{2}}[/tex] and [tex]\mathsf{y_m=\dfrac{y_1+y_2}{2}}[/tex]
where:
xₘ = x-coordinate of the midpoint
yₘ = y-coordinate of the midpoint
x₁ = x-coordinate of the first point
y₁ = y-coordinate of the first point
x₂ = x-coordinate of the second point
y₂ = y-coordinate of the second point
[tex]\\[/tex]
Solving for the center of the ellipse:
Let's say the first point is the first focus (-7, 6) and the second point is the second focus (-1, 6)
[tex]\mathsf{F_1=(-7,6)}[/tex]
x₁ = -7
y₁ = 6
[tex]\mathsf{F_2=(-1,6)}[/tex]
x₂ = -1
y₂ = 6
[tex]\\[/tex]
[tex]\mathsf{h=x_m=\dfrac{x_1+x_2}{2}}[/tex]
[tex]\mathsf{h=\dfrac{-7+(-1)}{2}}[/tex]
[tex]\mathsf{h=-4}[/tex]
[tex]\\[/tex]
[tex]\mathsf{k=y_m=\dfrac{y_1+y_2}{2}}[/tex]
[tex]\mathsf{k=\dfrac{6+6}{2}}[/tex]
[tex]\mathsf{k=6}[/tex]
[tex]\\[/tex]
The center of the ellipse is at (-4, 6)
[tex]\\[/tex]
The constant sum of the distances for any point from the foci, by definition, is the length of the major axis. The length of the major axis is equal to 2a.
2a = 14
[tex]\mathsf{a=\dfrac{14}{2}}[/tex]
a = 7
[tex]\\[/tex]
We already have the value of h, k and a. The only left is b. To solve for b, we know that the distance to one focus to the center of the ellipse is equal to c. If we solved to value of c we can use the relationship between a, b and c.
Relationship between a, b and c:
[tex]\mathsf{a^2=b^2+c^2}[/tex]
where:
a = semi-major axis
b = semi-minor axis
c = distance from the center to one focus
[tex]\\[/tex]
To solve for c, we can use the distance formula
Distance formula:
[tex]\mathsf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
where:
x₁ = x-coordinate of the first point
y₁ = y-coordinate of the first point
x₂ = x-coordinate of the second point
y₂ = y-coordinate of the second point
d = distance between the two points
[tex]\\[/tex]
Solving the distance between the center and one focus. Let's say the first point is our center (-4, 6) and the second point is the second focus (-1, 6).
Note: It doesn't matter what focus you use. The answer will be the same
[tex]\mathsf{C=(-4,6)}[/tex]
x₁ = -4
y₁ = 6
[tex]\mathsf{F_2=(-1,6)}[/tex]
x₂ = -1
y₂ = 6
[tex]\\[/tex]
Using the distance formula:
[tex]\mathsf{c=d=\sqrt{[-1-(-4)]^2+(6-6)^2}}[/tex]
c = 3
[tex]\\[/tex]
Using the relationship between a, b and c:
[tex]\mathsf{a^2=b^2+c^2}[/tex]
a = 7
c = 3
[tex]\\[/tex]
[tex]\mathsf{(7)^2=b^2+(3)^2}[/tex]
[tex]\mathsf{49=b^2+9}[/tex]
[tex]\mathsf{b^2=49-9}[/tex]
[tex]\mathsf{b=\sqrt{40}}[/tex]
[tex]\\[/tex]
Substituting the values of a, b, h, and k in our standard equation:
[tex]\mathsf{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
[tex]\mathsf{\dfrac{[x-(-4)]^2}{(7)^2}+\dfrac{(y-6)^2}{(\sqrt{40})^2}=1}[/tex]
[tex]\mathsf{\dfrac{(x+4)^2}{49}+\dfrac{(y-6)^2}{40}=1}[/tex] (ANSWER)
23. 3. The foci length of an ellipse is 4 and the distance from the point of an ellipse is 2 and 6 units from each foci respectively, calculate the equation of the ellipse if it is centered (0,0). non Sense answer report
_______________________________
Answer and solution nasa picture na po
24. What is Brahe’s observation on planet Marsmotion?(a) the orbit of Mars is circular and not an ellipse(b) the orbit of Mars is half circular and half ellipse(c) the orbit of Mars is not circular but an ellipse
Answer:
C. the orbit of Mars is not circular but an ellipse25. Find the standard equation of parabola opening to the left whose axis contains the major axis of the ellipse 4x² + 9y² = 144, whose focus is the centre of the ellipse, and which passes through the co-vertices of this ellipse.
Answer:
Ninety-Degree Push-up The object of this test is to measure strength of th Using an exercise mat or any clean mat, perfor number of properly executed push-up. Record yo 90° Push-up = repetitions
26. as you consider the shape of the graph of an ellipse where a=b, can you consider a circle as an ellipse? why or why not?
Answer:
A because she is absoarb math
27. Kepler's law that is also known as the law of ellipses and explains that the planets are orbiting the sun in a path described as an ellipse.
Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. ... The resulting shape will be an ellipse. An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points is a constant.
28. When examining scatterplot and draw an ellipse around the data, long and narrow ellipses means
Answer:
Strong linear association
Explanation:
29. an ellipse has an equation 25x²+16y²+150x-32y=159. Find the standard equation of all parabolas whose vertex is a focus of this ellipse and whose focus is a vertex of this ellipse
-4/5sqrt-y^2+2y+24-3
-4/5sqrt-y^2+2y+24-3
-4/5sqrt-y^2+2y+24-3
-4/5sqrt-y^2+2y+24-3
30. is a circle an ellipse?
Answer:
i think yes
Step-by-step explanation:
because a eclipse is circle i see a eclipse
