Find the orthogonal trajectories for the family of ellipses with centers at the origin and horizontal major axis equal to 2.

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

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Q: Find the family of curve that intersects the family of hyperbolas y² = 2x² +b at an angle arctan(1).

A: To find the family of the curve that intersects the family of hyperbolas y2=2x2+b at an angle…

Q: The solid whose base is the triangle with vertices (0, 0), (2, 0), and (0, 2), and whose cross…

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

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Q: A flashlight is shaped like a paraboloid and the light source is placed at the focus so that the…

A: Given the flashlight is shaped like a paraboloid and the light source is placed at the focus so that…

Q: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet.The…

A: Given: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100…

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 3x + y = 3 that are farthest away from the point (1, 0). %3D smaller…

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Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: Find three different parametrizations of the graph of y = x3.

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Q: Find the equation of the conic section indicated. Parabola with vertex (4, −1), directrix x = 15

A: Vertex is 4, -1 and directrix is x=15. Now vertex is, h, k=4, -1⇒h=4  &  k=-1 & Directrix…

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

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Q: Find a parametrization for the following curve. a.) The ellipse centered at (2,-3) whose major axis…

A: Here we find out parametric equation for ellipse.

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

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Q: Find the equation of one of the tangents to the ellipse 2x² + 4y² = 48 with slope of mt = 1.

A: The given equation of the ellipse is, 2x2+4y2=48 To find the slope of the tangent to the ellipse, we…

Q: Derive the orthogonal trajectories of the family of hyperbolas ??=?.

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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 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 point (x, y) on the ellipse, 4(x - 1)^2+ y^2 = 1, that is farthest to the origin (0, 0).

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Q: Maximize xyz on the ellipsoid

A: See the details solution in below

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

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (0, 5) and (0, 1). =D ?

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

A: I am going to solve the given problem by using the Lagrange's Multiplier method to get the highest…

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

A: Given that equation of ellipses 16x2+121y2=cTo find equation of orthiginal trajectarySolution if…

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 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: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (х, у) %3…

A: The distance between of two-points: - The length of the line segment connecting two places is the…

Q: Find the orthogonal trajectories of the family of parabola described by the equation (y – 3) = = cx…

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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: 1. Determine the orthogonal trajectories of the family of ellipses 16x? + 121y² = c. Sketch some of…

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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: (a) Where does the normal line to the ellipse x - xy + y²-3 at the point (-1, 1) intersect the…

A: To find next coordinate points of normal line to ellipse, find the derivative of given equation of…

Q: Find the dimensions of the rectangle with maximum perimeter that can be inscribed with sides…

A: Assume the length of rectangle be 2x and width of the rectangle be 2y. Therefore, the perimeter is…

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y² = c. Sketch some of…

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Q: What is the relation of the conic section to the perfume container?

A: Common Parts of Conic Sections While each type of conic section looks very different, they have some…

Q: 3. Find the family of orthogonal trajectories of the family of ellipses centered at the origin and…

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Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

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Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

A: The solution are next step

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

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Q: Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point…

A: We have to find the equation of the tangent plane to the hyperboloid x2-y2-z2=4 at the point 3,2,4.

Q: what is the equation of the geodesic in the hyperbdic upper half-plane that joins -1+i with Iti

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Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

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Q: A suspension bridge with weight uniformily distributed along its length has twin towers that extend…

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