3. Find the coordinates of the foci of the ellipse given by the equation 4x² + y? = 64. O (0, 4v3) and (0, –4v3) | О (, 48) and (0, — 48) О (,4) and (0, —4) O (4/3, 0) and (-4v3, 0)

Q: Find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme values.

A:

Q: What is the length of the minor axis of the ellipse 4x² + 32x + y² – 4y + 52 = 0? 0 4/3 0 4 0 8 O 45

A: Topic = Ellipse

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A: The standard form of an ellipse is [(x – c1)2 / a2 ] + [(y- c2)2 / b2 ] = 1 Where (x, y) –…

Q: 14. Find the maximum and minimum values of the function f(x,y) y? = xy on the ellipse given by the…

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Q: 6. What is the equation of the ellipse whose graph is shown below? (1,4) (7. 0) C(1,0) (4, -54 3 A)…

A: Graph of the ellipse is given, we have to find its equation

Q: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given y? by the…

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Q: 27. Find the points on the ellipse 4x? + y? away from the point (1, 0).enigsmuo 4 that are farthest…

A: Given: The equation of ellipse is given as, 4x2+y2=4. The objective is to find the point x,y on the…

Q: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given y? by the…

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Q: Write the equation of an ellipse centered at (1, -2) whose minor axis has length 6 and horizontal…

A: We can find the equation of ellipse using the given data as below.

Q: 7. Write the equation of the ellipse with a minor axis length of 8 units and foci at (-7, 4) and…

A:

Q: 4. §yʻ dz + 2ry³ dy, where C is the ellipse z + 2y? = 2.

A: To Determine: find the integral  Given: ∮y4dx+2xy3dy where C is the ellipse x2+2y2=2 Explanation: we…

Q: +1. Give the coordinates of the center, vertices, covertices, and foci of the ellipse with the given…

A:

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

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Q: Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed…

A: Let the dimension of such a rectangle be 2x by 2y. Clearly (x, y) is point on the ellipse.

Q: 1. Find the maximum and minimum distance from the origin to the ellipse 2² + xy + y² = 3

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Q: Find the equation of the horizontal ellipse that is centered at ( 27 , 18), passes through the point…

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Q: 4) Consider the ellipse x? – xy + y? = 3. From all points (x, y) of this ellipse, find: 1. the ones…

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Q: What is the equation of the ellipse with the center at (0.0) that passes through the points (2,0),…

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Q: 23 +z+1 Evaluate -dz , where C is the ellipse 4x + 9y² = 1. c z² – 3z +2

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Q: 1. Find the minimum and maximum values of f(x,y) : = x²y on the ellipse 4x? + 9y? = 36. %3D

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Q: 1. Give the coordinates of the center, vertices, covertices, and foci of the ellipse with the given…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: 26. Find the standard form of the equation of the specified ellipse. Foci: (1, 5), (-3, 5); Major…

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Q: 19. The center of the ellipse 4x2 + y2 -16x - 6y – 43 = 0 is at: %3D

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Q: Find an equation of the ellipse with foci at (-4, 3) and (-4, –9) and whose major axis has length…

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Q: 7. Find an equation in standard form for the ellipse with center at (5,7), horizontal major axis of…

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Q: 7. Write the equation of the ellipse in standard form. 8x +32x + 4y – 8y = -4 (+2)2 4 (y+1)? =1 8 O…

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Q: Compute the length of the latus rectum of the ellipse x2 + 2y2 +4x+ 4y +4=0

A: Given:    x2 + 2y2 +4x+ 4y +4=0

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Q: Find the standard form of the equation of the ellipse with the given characteristics. y 1아 (7,8) 8…

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Q: |The length of the latus rectum of the ellipse defined by 25x²+9y² – 300x – 144 y + 1251 = 0 is А.…

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Q: What are the foci of the ellipse given by (z-3)2 (y-1)2 - = 1? 25 O (-4, 1) and (4, 1) O (3, 5) and…

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Q: Find the minimum and maximum values of f(x, y) = x2y on the ellipse 4x2 + 9y2 = 36.

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Q: 4. Find the equation of the ellipse with vertices at (2, -1) and (2, 7) and with a minor axis of…

A: We have to find equation of ellipse with given vertices and minor axis.

Q: 1. Write the equation of the ellipse with endpoints of the major axis (-11, 0) and (11, 0) and minor…

A: Topic- Conic section

Q: 5. What is the general form of an ellipse with foci at (0, +2), and vertices at (0, ±4)? 2x + 4y = 0…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 18. Write the equation of the ellipse with a minor axis length of 8 units and foci at (-7, 4) and…

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Q: Find the standard form of the equation of the specified ellipse. 28. Foci: (6, 2), (0, 2); Major…

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Q: Which is the equation of an ellipse with direcrices at x = =-4 and foci at (2,0) and (-2,0)

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Q: 4. (a) Derive the equation of the ellipse z+=1 b² =1. a

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.