Given a plane 2y + 4z = 5 intersects the cone z^2 = x^2 + y^2 in an ellipse. Find the points on this ellipse the closest to the origin.

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: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: Sketch the surface..........CYLINDERS.............x2 + 4z2 = 16

A: Here we have to draw the surface of cylinder having equation  x2+4z2=16

Q: Find the distance between the point (1, 0, 2) and the plane 2x – 3y + 6z = 6.

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, –3, 4) Radius:…

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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) =…

A: We have to find the point which is farthest away from the point 1,0 at the ellipse: 4x2+y2=4 Writing…

Q: IS filled with circley The world around us Para bolas , e llipses and hyperbolas, In your post…

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

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

Q: Find the distance between the point (3,4,5) and the plane 2x + 4y 3z = 12.

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Q: Identify the quadric surface. 9x2 + y2 – 9z2 - 54x – 4y – 54z + 4 = 0 O hyperboloid of two sheets O…

A: Identification of quadratic surface

Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

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Q: center, horizontally, is the car when it is at an altituue Ul 23 IL! 2. A truck has to pass under an…

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

A: Given information: The cables touch the road surface at the center of the bridge, Then image a graph…

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

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Q: Find the distance between the point (1, 3, −1) and the plane 3x − 4y + 5z = 6.

A: According to the question, we have to find the distance between the points 1,3,-1and the plane…

Q: What are the lengths of the major and minor axes of this ellipse 6 =D1? O Major Axis: 6 units, Minor…

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

A: The general equation for a parabola is given as, y=kx2 Let the x-axis represents the road surface…

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: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y + = 3 and the paraboloidz =…

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Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/22^2 + y^2/10^2 = 1. The…

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Q: Find the distance from the point (-3, 4, -1) to the plane 5x−4y−5z=−3.

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Q: Find an equation of the sphere with center (2,-3,6) that touches the xy-plane.

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Q: Find the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

Q: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and…

A: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotating it out of the xy-plane and around…

Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 + 2z2 −…

A: The quadric surface given to us is: x2+y2+2z2-2xy+4xz+4yz=16 This is compared to the general form of…

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, =7,2) Radius:…

A: Explanation of the answer is as follows

Q: Let S be the quadric with equation 36x² –4y² –9z² – 36x = 0. Sketch a graph of the surface with…

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Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

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Q: Find the distance from the point (1, -4, 4) to the plane −2x−4y+3z=5

A: Given:The point (1, –4,4) and the equation of the plane –2x–4y+3z=5.The distance from the point…

Q: A mirror for a reflecting telescope has the shape of a finite paraboloid of diameter 0.3 meters and…

A: Equation of a circular paraboloid  f=r24d here, f= focal length along the axis of symmetry from the…

Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

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Q: Find an equation of the sphere with center (-3, 2,5) and radius 4. What is the intersection of this…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, –3, 5) Radius:…

A: Given that: Centre of the sphere, (h,k,g)= (-1, -3, 5) and radius, R=6

Q: Find the volumes of the solids generated if the upper half of the ellipse 9x2 + 25y2 = 225 is…

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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: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and…

A: To answer it, let us go through the equation of Hyperboloid of 2 sheets   x2a2 - y2b2  - z2c2 = 1…

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

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Q: Find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5 Thank you.

A: To find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5

Q: Find the points on the curve of intersection of the ellipsoid x²+4y²+4z²=4 and the plane x-4y-z=0…

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Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

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: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

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Q: Find the distance between the point (1, 0, 2) and the plane 2x − 3y + 6z = 6.

A: To find the distance

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

A:

Q: Find the standard equation of the sphere with the given characteristics. Center: (−1, −5, 8);…

A: The Center of the sphere is (−1, −5, 8) and Radius: 5

Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

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