Consider the ellipse given by the intersection of the plane x+y+7z=3 with the paraboloid x^2+y^2=2z. Find the point on this ellipse that is farthest from the origin. Provide the x-coordinate of this point in response.

Q: Find a parametric description for the ellipse 9x2+4y2+24y=0 oriented clockwise.

A: Ellipse

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: 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: A mirror is shaped like a paraboloid of revolution and will be used to concentrate the rays of the…

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Q: What is the relation of the conic section to the vase?

A: Let's find.

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

A: Given a plane x+y+2z=2 intersects the paraboloid z=x2+y2 in an ellipse We need to find the points on…

Q: Find an equation for the surface obtained by rotating the parabola y=2 about the y-axis.

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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: 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: What is the relation of the conic section to the oblong plate?

A: Key Points A conic section (or simply conic) is a curve obtained as the intersection of the surface…

Q: The hyperbola in Position I opening up opening down in Position II y² x² 4 16 1 is

A: Topic :- geometry

Q: What are the parametric equations for an ellipse centered at the origin with a major axis of length…

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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: Consider the two ellipses in the x y plane given by the equations (x-1)2 2 =1 and (x+2)2 (y-5)2 62…

A: Given:  The given ellipse equations are x-1262+y232=1and x+2222+y-5242=1

Q: A mirror is shaped like a paraboloid of revolution and will be used to concentrate the rays of the…

A: It is given that The cross-section is a parabola. Let the vertex of the parabola be at the origin of…

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: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: Determine the equation of ellipse in standard form with center (2,3), semi-major axis is 5, vertical…

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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: What is the equation in standard form of an ellipse whose center is at C(-3, 1), a vertex at V(-5,…

A: NOTE: Refresh your page if you can't see any equations. . the standard form of the ellipse is given…

Q: Calculate the curvature of the ellipse x2a2+y2b2=1 at its vertices.

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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…

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Q: Find the standard equation of the ellipse whose major and minor axes are the transverse and…

A: We need to find standard equation of ellipse.

Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. O elliptic…

A: To identify the surface that corresponds to given equation- 100y2-25x2-4z2=1.

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

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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

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

A:

Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 ,…

A: \ Revolution of the hyperbola about its transverse axis generates a surface of two sheets, two…

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: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 +y^2/11^2=1. The…

A: Explained below

Q: Calculate the curvature of the ellipse x2 / a2+y2/b2=1 at its vertices.

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Q: A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and…

A: It is given that, A mirror for a reflecting telescope has the shape of a (finite) paraboloid of…

Q: Prove that the surface of the given equation is an ellipsoid. Hence, determine its center. 9x +4y…

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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: 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: The length of the latus rectum of the ellipse defined by 25x2 +9y2 - 300x – 144 y + 1251 = 0 is 3.0…

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Q: Find the surface area of the ellipsoid obtained by rotating the ellipse (=) = 1 about the x-axis.

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

Q: Find the equation of the horizontal ellipse that is centered at ( 15, 10), passes through the point…

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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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