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: dentify the equation of the ellipse that has the coordinates of its center C (5, 1), the coordinates…

A: Given that: Centre of ellipse=(5, 1)Coordinates of vertex=(5, 4)Coordinates of minor axis =(3,1)

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: Find the equation to the ellipse whose centre is at the origin and the axes are the axes of…

A:

Q: What is the center of an ellipse 64x2 + 25y2 = 1600? a.2,3                                     b.…

A: Use the standard equation of ellipse  for finding the center.

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

Q: Determine endpoints of the major and of the minor axes of the ellipse described by the equation…

A: standard form of an ellipse is, (x-h)2a2+y-k2b2=1 where (h, k) is the center of ellipse, end-points…

Q: Write the equation of the ellipse 4x2 + 36y² + 16x - 72y - 92 0 in standar form where: h = k = a =…

A:

Q: Find the equation of the ellipse x2 + 9y2 - 4x - 72y + 139 = 0 and locate the coordinates of the…

A: Given the equation of the ellipse, x2+9y2-4x-72y+139=0