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

Q: Determine the greatest and least distance from the origin to a point on the ellipsoid 9x2+4y2+z2=36

A: Here is the solution of the given problem. Application of Lagranges Multiplayer.

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

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y? = c. Sketch some of…

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Q: 4. The upper half of the ellipse centered at the origin with axes of length 2a and 2b is described…

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Q: Find the standard form of the equation of the specified ellipse. 19. Foci: (0, –4). (-4, – 4); Major…

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Q: What is the equation of an ellipse with its center at (-2, 1), a major axis 16 units long, and…

A: Write equation of parabola

Q: The question is about Lagrange multipliers. Use the Lagrange multipler method to locate the point on…

A: The question is about Lagrange multipliers. Use the Lagrange multipler method to locate the point on…

Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices:…

A: Here the vertices of the ellipse is with a constant x-coordinate. Therefore the given ellipse is…

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (x,y)=(?)…

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Q: 57. Use a change of variables to prove that the area of the ellipse with equation (-) + ) : -1 is…

A: Explanation: Given that, the standard equation of the ellipse is: x2a2+y2b2=1 Solve for…

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). %3D smaller…

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Q: Find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy +…

A: To find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy…

Q: Find the orthogonal trajectories for the family of ellipses with centers at the origin and…

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Q: Find the length of major axis of the ellipse x^2+4y^2-2x-8y+1=0

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Q: Find an equation of the ellipse with foci at (−3,7)and (−3,−3) and whose major axis has length 20.…

A: The foci of the ellipse is (−3,7)and (−3,−3). The length of the major axis is 20.

Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 + y^2/12^2 = 1. The…

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Q: What is the highest point on the ellipse that is the intersection of the plane x + y + 2z = 2 and…

A: Given  the intersection of the plane x+y+2z=2 and the paraboloid z=x2+y2

Q: Determine the orthogonal trajectories of the family of ellipses 16x² + 121y² = C. Sketch some of the…

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Q: Find the envelope of the family of ellipses defined by the equation x2/a2+y2/b2=1 provided that…

A: The equation of the family of ellipses is given by provided that  So, the equation of family of…

Q: Find the point on the ellipse 4x2ty3=4 that are farthest away from the point (1,0) 4x27y2-4

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Q: Find the envelope of the family of ellipses defined by the equation x2a2+y2b2=1 provided that…

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

A: 1) To Find: The maximum and minimum distance from the origin to the ellipse x2+xy+y2=3. As per…

Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z=2 and the…

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Q: By integration, show that : 8. The area of an ellipse with semi axes a and b is A = nab.

A: Integration of function expression with respect to x or y gives the area under function curve and…

Q: 3. Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes…

A: Let vertex of the rectangle be x,y, x,-y, -x,y and -x,-y. Thus, are of the rectangle is fx,y=4xy. We…

Q: Find the larger dimension of this rectangle. If a rectangle of maximum perimeter is to be inscibed…

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Q: What is the maximum area of a rectangle inscribed in the ellipse 25 + y? = 1?

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Q: Find the area inside the ellipse x2a2+y2b2=1.

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Q: Find the length, breadth of the rectangular box of maximum area that can be inscribed in the ellipse…

A: The area of a rectangle is Area=Length × Breadth The area is maximum if the second derivative of…

Q: Prove that the product of the perpendicular distances F1R1 and F2R2 from the foci to a tangent line…

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Q: A stationary artist intends to make rectangular cut-outs from the elliptical cardboard that he has.…

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Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

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Q: A one-way tunnel has the shape of a semi ellipse that is 12ft high at the center and 28H across. a.…

A: If the semi-ellipse is 12ft high at the center and 28 ft across then  The length of the major axis,…

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

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Q: The length of the major axis of the cllipse with center (-4, 1), minor axis parallel to the y-axis…

A: Equation of ellipse with center (-4,1) is given by

Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: What is the maximum area of a rectangle inscribed in the ellipse defined by x2/64 + y2/25 = 1? Enter…

A: Let the length and breadth of the rectangle as x, y respectively Area of rectangle = xy Now…

Q: Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that…

A: Given equation 2x2+72y2=72which can be writtenx236+y21=1

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: 2. What are the foci of this ellipse? 5 -5 O (-1, –4V5) and (–1, 4v5) O (-1, –2/5) and (-1,2/5) O…

A: By carefully examining the figure we will find that the major axis should pass through the line x =…

Q: Find an equation of the ellipse with foci at (-5,9) and (-5,-10) and whose major axis has length 22.…

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Q: Find the envelope of the family of ellipses x2a2+y2b2=1 having the same area.

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Q: Find the maximum and minimum values of f(x, y) = 7x + y on the ellipse x2 + 9y² = 1

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Q: Find the points on the ellipse 3x² + y“ = 3 that are farthest away from the point (1, 0).

A: For the Given Ellipse 3X2+y2=3 ,Points that are  Farthest away from the point (1,0) is calculated as…

Q: Sketch the conic sections. Indicate the foci, and show your work: A) 4x2+3y2+8x-6y=5 B)…

A: A)Given equation is,

Q: Find the maximum and minimum values of f(x, y) 3x+y on the ellipse +25 = 1 %3D maximum value:

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Q: Find the dimension of the rectangle of maximum area that can be inscribed in the ellipse…

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Q: Find the envelope of the family of ellipses x2/a2+y2/b2=1 having the same area.

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Q: What is the standard form of the ellipse with center at (0,0),vertex at (0,9) and co vertex (4,0)

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Q: Sana wants to recycle some elliptic cardboard into rectangular name plates. The minor and major axes…

A: Given problem is : Sana wants to recycle some elliptic cardboard into rectangular name plates. The…