Find an equation of the sphere containing all surface points P = (x, y, z)  such that the distance from P  to  A(−2, 6, 2)  is twice the distance from P  to  B(4, 3, −1).

Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: Find the maximum and minimum values of ƒ(x, y, z) = x - 2y + 5z on the sphere x2 + y2 + z2 = 30.

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Q: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

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Q: If a parametric surface given by r₁ (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -2 ≤ u ≤ 2, -3 ≤ v ≤…

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Q: Determine the points on the surface y2+z2−x=8 that are closer to the origin.

A: Consider the given surface. y2+z2−x=8z2=8−y2+xf(x,y)=8−y2+x

Q: parametrizes the portion of the sphere x² + y² + z² = 9 that is above the xy-plane and below the…

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Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Let C be the curve of intersection of the parabolic cylinder x² = 2y, and the surface 3z = xy. Find…

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Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

Q: A 2-D surface was found in one research group of scientists and a surface equation has been derived…

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Q: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: Find the area of the surfaces The surface cut from the bottom of the paraboloid z = x2 + y2 bythe…

A: The formula for the surfaces area of the paraboloid above the region R is: A=∬Rzx2+zy2+1dxdy Where,…

Q: Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the…

A: Let d1 be the distance from the point 0,0,1 to the point Px,y,z and d2 be the distance from the…

Q: Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 +…

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Q: Find a parameterization for the quarter sphere x² + y² + z² = a² where z > 0 and x > 0.

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Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: Find the points on the sphere x +y +z = 154 where f(x,y,z) = 3x + 8y + 9z has its maximum and…

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Q: If the maximum distance from the surface x? + 2y² + z? = 3 to the point (1,0, –1) is Va+ bv6, what…

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Q: Find the area of the surface. The part of the paraboloid z = 1 – x² – y2 that lies above the plane z…

A: Givenz=1-x2-y2z=-2Suppose the surface is defined byz=f(x,y) for x∈R, then the area of the surface is…

Q: (a) Show that the two surfaces S₁: z = xy and S₂ : z = ³x² - y² intersect perpendicularly at the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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Q: Find the area of the part of the sphere x2 + y? + z² = 4z that lies inside the paraboloid z = x2 +…

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Q: Find the point lying on the intersection of the plane x + y + 4 z = 0 and the sphere x2 + y2 + z2 =…

A: Determine z from the equation of plane.

Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…

A: We will find out the required value.

Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: Find the center C and the radius r of the sphere S: x2 + y2 + z2 + 4x + 8y – 8z =-11

A: A geometrical object which is in the shape of ball is called sphere. Outer surface of sphere is…

Q: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

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Q: Find the surface which intersects the surfaces of the system z(x+ y) =c(3z+1) orthogonally and…

A: To finding the surface which is intersecting given system and orthogonal to circle is given as…

Q: Find the point on the surface r – 2xy + 2y² – x+ y = 0 closest to the point (1, 2, –3).

A: Consider the provided question, We have to find the point on the given surface closest to the point…

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y° and z = 25 – x² – y² .

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Q: Find the maximum value of f(x,y,z)=24x+18y+21z on the sphere x²+y²+z²=49 I

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Q: The part of the sphere x^2+y^2+z^2=4z that lies inside the paraboloid z=x^2+y^2

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Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: The equation of the sphere with radius r = V75 and center C(2,1, – 1) is (a) x² + y² + z² + 4x + 2y…

A: The general equation of a sphere with radius r and center a,b,c is x-a2 + y-b2 + z-c2 = r2

Q: Find the center and radius of the sphere. 2 4x + 4y + 4z + x + y+z= 25

A: Topic = Sphere

Q: Let C be the curve of intersection of the parabolic cylinder x? = 2y, and the surface 3z = xy. Find…

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Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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Q: Let 11 be the surface with the equation = 2√y+1 and let 12 be the sphere with equation x²+y+z² 16x +…

A: Given data÷ Find the center and radius of the sphere   x2+y2+z2-16x+16y-4z+76=0   General form of…

Q: Find the area of the surface. The part of the paraboloid z = 1 - x² – y2 that lies above the plane z…

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Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

Q: Find the extreme values of f(x,y,z) = x-yz + 1 on the intersection of the plane z= 3 with the sphere…

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