Find the points on the sphere at which the minimum and maximum distances between the sphere x2+y2+z2= 58 and the point (2,3,4) occur.

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Sketch the surface.......... ASSORTED ............... 4y2 + z2 - 4x2 = 4

A: Given :             The given function is 4y2 + z2 - 4x2 = 4 And can be written as,…

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

A:

Q: 3. Identify and sketch the surface given by z = 16-y²; 0 ≤ y ≤ 2; 0≤x≤ 4. in 3-space, include ALL…

A:

Q: Sketch the surface.......... ASSORTED ............... x2 + z2 = 1

A:

Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: Find equations of the spheres with center (2, −3, 6) that touch (a) the xy-plane, (b) the yzplane,…

A: To find the equations of the spheres with center (2, −3, 6) that touch (a) the xy-plane, (b) the…

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: Find the minimum and maximum squared distance between the sphere x² + y² + z² = 9 and the point…

A: We have to find the minimum and maximum squared distances between the sphere x2+y2+z2=9 and the…

Q: Classify the surface: 1-z = 3y? + 4z? ,2

A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

Q: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A:

Q: Sketch the surfaces PARABOLOIDS AND CONES z = 8 - x2 - y2

A: Consider the equation of the surface, z = 8 - x2 - y2

Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

A:

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

A:

Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: Find the center C and the radius a for the sphere 1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9 2. x2 + y2 + z2 -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the standard equation of the sphere with the given characteristics. Center: (−4, 0, 0), tangent…

A:

Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

A:

Q: Find the center C and the radius a for the spheres 2x2 + 2y2 + 2z2 + x + y + z = 9

A: General equation of a sphere, x2+y2+z2+2ux+2vy+2wz+d=0 Centre of sphere = -u, -v, -w Radius of…

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

A:

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

A:

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z² 24 and the paraboloid…

A:

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: Find the area of the part of the surface z = x² + 2y that lies above the triangle with vertices…

A:

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 minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Let 11 be the surface with the equation = 2√/y+1 and let 12 be the sphere with 2 equation x²+ y²¹+…

A: Solution :-

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

A:

Q: Find and classify all the critical points of the surface with its equation z = 3x"y + y* – 3x2 – 3y?…

A:

Q: Find the equations of all spheres in R 3 of radius R = 3 passing through the point (7 ,8, 9) that…

A: To find the equation of spheres Given that, from the question  Radius R = 3  with Passing through…

Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: Sketch the surfaces PARABOLOIDS AND CONES x = 4 - 4y2 - z2

A: The given equation is x = 4 - 4y2 - z2

Q: Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian…

A: Let fa,b,c=a2b2c2 subject to a2+b2+c2 =r2  The gradient equation is…

Q: classify the quadric surface given by equation and determine its standard form.−8x 2 − 8y2 + 10z2 +…

A: We have the quadratic surface : -8x2-8y2+10z2+32xy-4xz-4yz-24=0…

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

A:

Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Find out the nature of the surfaces 2x +3y² +z² –8x+6y-4z-3=0 and compute their centers and lengths…

A:

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

A:

Q: 6. The part of the surface z = 1 + 3x + 2y² that lies above the triangle with vertices (0, 0), (0,…

A: Given: A surface z=1+3x+2y2 and vertices of triangle (0, 0), (0, 1) and (2, 1). To find: Area of…

Q: Find and classify all the critical points of the surface with its equation 2 = 3a²y + y3 – 3x² – 3y?…

A:

Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

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

A:

Q: Show that the maximum value of abc on a sphere of radius r centered at the origin of a Cartesian…

A:

Q: 2) Find the area of the part of the surface z = x2 + 2y that lies above the triangle with vertices…

A: