nts, in a line, or in a circle? sphere intersects the xz-plane ? sphere intersects the yz-plane ?

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: A quadratic surface has the equation x2+2y2+2z2+2yz = 1. Write the equation in standard form.…

A: To write the quadratic surface equation \( x^2 + 2y^2 + 2z^2 + 2yz = 1 \) in standard form and…

Q: 5. Find the standard form equation of a sphere that has a diameter with endpoints (3, -2, 4) and (7,…

A: Given : The end points of a diameter of a sphere are  (3, -2, 4) and (7, 1, 4). To find : We have to…

Q: What is the equation for a sphere centered at the point (4,-3,-7) with a radius of 5.

A: The general equation for a sphere in three dimensions is given by (x - h)^2 + (y - k)^2 + (z - l)^2…

Q: Find the dot product: (-1, 0,1) . (1, 9, 2). Fully reduce your answer. (It should be a whole number)

A: To find The dot product of (-1,0,1).(1,9,2)

Q: atelite dish ha

A: The equation of the parabola is x2=4ay. Where, a is the focal length of the parabola.