The plane x+ y+2z =2 intersects the paraboloid z = x2+y² in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin.

Q: Find the coordinates of the foci of an ellipse with center at (-1,2), one co-vertex at (2,2), and…

A: Given problem:- Find the coordinates of the foci of an ellipse with center at (-1,2), one co-vertex…

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

A: Note that here we have to extremize x2+y2+z2 , whch is eqivalently ,to extrimize x2+y2+z2.

Q: The quadric surface, * - a - = 1 l is a hyperboloid %3D 64 None of these of one sheet that opens…

A: The given quadratic surface is: x24-y264-z216=1

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

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Q: The plane 15x + 20y + 40z = 195 intersects the cone z = x² + y² in an ellipse. The sum of the…

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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: ind the points on the ellipse  5x2 + y2 = 5  that are farthest away from the point (1, 0). smaller…

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Q: The plane 9x + 12y + 40z = 275 intersects the cone z? = x² + y? in an ellipse. The sum of the…

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Q: The plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. Find the points on…

A: Given the plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. We need to…

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 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: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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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: 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: The equation x2 + xy + y² = 1 determines an below. ellipse in the xy-plane shown

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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: Find the points on the ellipse  X^2 + 6y^2 + 3xy =40 With the greatest x coordinator

A: Let us assume thatfx,y=xandgx,y=x2+6y2+3xy-40The lagrange multiplier equations…

Q: The reflector of a searchlight is in the shape of a paraboloid of revolution. Its diameter is 16…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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: The plane 6x + 8y + 60z = 700 intersects the cone z = x + y in an ellipse. The sum of the z-…

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Q: find the perimeter of the ellipse x2/a2 + y2/b2 = 1.

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Q: A searchlight is shaped like a paraboloid of revolution.If the light source is located 2 feet from…

A: draw the parabola used to form the searchlight on a rectangular coordinate system so that the vertex…

Q: Find the largest triangle that can be inscribed in the ellipse (x2/a2)+(y2/b2)=1 using Lagrange…

A: answer is in next step

Q: The plane 9x + 12y+ 40z = 275 intersects the cone z = coordinates of the highest and lowest points…

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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: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given %3D y? by the…

A: Given :  The function f ( x, y ) = x y and the ellipse  x2 + y24 = 1.   To determine :  The maximum…

Q: Find the point on the ellipse x2 + 6y² + 3xy = 40 with the largest x-coordinate (Figure ). -8 FIGURE…

A: Given: x2+6y2+3xy=40

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 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 equation of the ellipse with the center at (0,0) that passes through the points (2,0),…

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Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

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: The plane x + y + 2z = 6 intersects the paraboloid z = x2 + y² in an ellipse. Find the points on…

A: To find the farthest and nearest point from the origin to the ellipse.

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 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 maximum and minimum values of f(x,y)=xy on the ellipse  4x^2+y^2=6

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Q: The plane 9x + 12y + 40z = 275 intersects the cone z² = x2 + y2 in an ellipse. The sum of the…

A: We have to find the sum of the z coordinates of the highest and lowest points on the ellipse. This…

Q: Find the center of the ellipse given by x² – 2x + 2y? - 12y +3 0. Enter as an ordered pair without…

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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: Consider the ellipse given by the intersection of the plane x+y+7z=3 with the paraboloid x^2+y^2=2z.…

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

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Q: The plane 12z + 16y + 60z 640 intersects the cone z2 = x² +y² in an ellipse. The sum of the…

A: Given 12x+16y+60z=640 z2=x2+y2

Q: Evaluate –dz , where C is the ellipse 4x² + 9y? = 1. %3D Yc z2 – 3z+2

A: Given: The equation: ∮C z3 + z + 1z2 - 3z +2dz Here C - ellipse of 4x2 + 9y2 = 1

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: For the Paraboloid,z-axis is it's Principal Axis,Also, it is symmetric with the lines x = 0 (yz…

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

A: Let,f(x)=x2+y2-z=0and g(x)=x+2y+2z=2Our constraint is,∇f(x)=λ∇g(x)

Q: boloid z=x^2+y^2 in an ellipse. Find the points on this ellipse that are nearest to and farthest…

A: In this question, the concept of Lagrange Multiplier is applied. Lagrange Multiplier The Lagrange…

Q: The ellipse 15x^2+2x+y^2=1 has its center at the point (b,c) where b = c=

A: To find the center at the point b, c of the ellipse,15x2+2x+y2=1b=?c=?