The plane x + y + 2z = 6 intersects the paraboloid z = x2 + y² in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin. Point farthest away occurs at ). Point nearest occurs at ).

Q: Consider the paraboloid given by the equation z = x^2 + y^2. Find the coordinates of the vertex and…

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center. The given…

Q: write the equation of the ellipse 9x2+36y2+90x+216y+225= 0 in standard form, please show all written…

A: Standard equation of ellipse is x-x02a2+y-y02b2=1    when major axis on the horizontal axis

Q: Find the equation of the ellipse in standard form centered with foci located at the (4, -5) and (-8,…

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Q: Find an equation of the ellipse that has center (-5, 5), a minor axis of length 6, and a vertex at…

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Q: What is the equation of an ellipse having vertices at and a minor axis (0,+8,) which is 6 units in…

A: the standard equation of the vertical ellipse is given by x-h2a2+y-k2b2=1

Q: State whether the equation z - ()² = (+)² defines a hyperboloid of two sheets. an ellipsoid. a…

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Q: 1. Find general solutions to the following systems. Feel free to use Wolfram Alpha to get the Jordan…

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