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

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

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Q: What is the differential equation of the family of ellipses with their centers origin and their…

A: Let us solve the problem using the basic equation of ellipse  later we will use different methods to…

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Find the points on the ellipse 2x + 4y = 1 where f(x.y) = xy has its extreme values.

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Q: Show that the line b2xx1 + a2yy1 - a2b2 = 0 is tangent to the ellipse b2x2 + a2y2 - a2b2 = 0 at the…

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Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

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Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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Q: Find equations of both the tangent lines to the ellipse  x2 + 4y2 =36 that pass through the point…

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Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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Q: 2 Find pxV 1+ 3x² dr, where P is the ellipse parametrized as follows: r(t) = , 0<t< 2n

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Q: 2. Evaluate dy, where C is the part of the parabola y = x² from (1, 1) to (2, 4).

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Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: Find the minimum of f(x,y) = 3x + 3y on the ellipsoid 3x2 + 3y = 2. Leave your answer correct to two…

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

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Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

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Q: Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

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Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

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Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.

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Q: Need some help with Greens Theorem and ellipse plz, thanks

A: It is required to calculate the value of the integral using green’s theorem:

Q: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)?

A: the equation of the normal line to the ellipse can be found by differentiating the given equation…

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x)) and C is the curve in the third quadrant from…

A: Given

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: 3. he tangent to the ellipse I at the point P: V2 4. 3. 3w q(w) = 2w+ V2 %3D 3 q(w) = 3w V2w - V2 3…

A: Ellipse tangent

Q: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 +…

A: It is required to find the equation of generating curve given the equation of its surface of…

Q: 8. Find the equation of the surface of revolution if the generating curve, 2x – 4y = 6 is revolved…

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Q: (a) Where does the normal line to the ellipse x2- x   y + y 2 = 3 at the point (1, -1) intersect the…

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Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

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Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: Use Lagrange multipliers to find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme…

A: This question is related to Lagrange multipliers theorem. We will solve this question by using…

Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: Find an equation for the tangent plane to the hyperboloid x2+y2−z2=1 at the point (3,1,3).

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Q: Find the extreme value of the function f(x, y) = xyon the ellipse x2 + 2y2 = 1.

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Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Find the points on the curve of intersection of the ellipsoid x² + 4y² + 4z² = 4 and the plane x –…

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Q: Find the maximum and minimum valves of f(xy)=5x+Y on the ellipse X+36y=!

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Q: Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

A: We need to find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of…

A: Given that the curve of intersection of the parabolic cylindery=x2 and the top half of the ellipsoid…

Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

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Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: Find the tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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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.