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

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

A:

Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

A:

Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin²z, z = [0, π]

A: Any point on the 3D plane is represented using the ordered pair: x, y, z. A graphing utility can be…

Q: 39. Find the surface area of the portion of the hyperbolic paraboloid r(u, v) = (u+ v) i + (u – v)…

A:

Q: Consider the surface given by the equation z – y = x². Draw a total of at least 3 traces in at least…

A: It can be solved in 2nd part using simple geometry.

Q: Describe and sketch the surface (x2/16) + (y2/9) + z2 = 1

A:

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: Given: x2+y42+z2=1  ……1   Equation of plane is: z=14  ……2

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 - Select a correct name for this surface and point…

A:

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: Find the points on the surface x2 - zy = 4 closest to the origin.

A:

Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

A:

Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

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

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

Q: sketch the given surface. x2 − 4y2 = z

A: Given: x2-4y2=z Divide the equation both sides by 4. x24-4y24=z4x222-y21=z4 The equation…

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

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

A:

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

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

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

Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder x² + (y − 1)² = 1.…

A: For the given curve we have the following vector valued function: R⇀=2cost. 1+sint,…

Q: Find an equation for the surface consisting of all points that are equidistant from the point (0,-…

A: Point (0, -3,0) Y= 3

Q: Sketch the section of the surface at y = 0. 1 + x² + y² Z = 4 -8 -6 -4 -2 4 4 6. 4 -8 -6 -4 -2 2. 4…

A: Given data is: To sketch the surface at y=0 z=1+x2+y2

Q: Sketch the surface r = 2y? + 32².

A:

Q: the trace of the surface in the plane x=1?

A:

Q: 2? = a? + 2y?

A: Consider the given surface z2=x2+2y2 The trace in the plane x=k are z2-2y2=k2 For k=0, z2-2y2=0⇒…

Q: Find an equation for the surface obtained by rotating the line z = 2x about the z-axis. + x²) b. z?…

A:

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

A: Given: x2 + y2 − z 2= 1

Q: Sketch and label the level surfaces of g(r, y, z) =1-r² – y² for g = 0,-1,-2.

A:

Q: Check whether the given surface (x – a)² + (y – b)² + (z – c)? 16 is developable or not. -

A: Given surface(x-a)2+(y-b)2+(z-c)2=16orz=c+16-(x-a)2-(y-b)2If the surface is developable…

Q: For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola.…

A: We have been given the equation  4x² + y² −z = 0           (1)

Q: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the…

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: 3. Use polar coordinates to find the surface area of the paraboloid z = x² +y² – 5 that lies below…

A:

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: Locate and classify the stationary points on the surface z=xy2-2xy-2x2-3x, remembering that  x, y ,…

A: Solving for stationary points of given function using partial derivatives

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

A:

Q: What are the reace curves of this surface for x=0, y=0, and for z=k? Name the shape of the surface.…

A: Note : In the question it has to be '' trace curves '' instead of '' reace curves ''. So, we are…

Q: Sketch the portion of the surface that lies in the first octant: y = z. 0.15 0.a 0.1 0. 0.15 0.18

A: To sketch the portion of the surface y=z that lies in the first octant. The sketch of y=z is:

Q: The surface x2 + y² = z² is identified as O A. Paraboloid O B. Cone O C. Hyperboloid of one sheet O…

A: the correct answer is option: D .) Hyperboloid of 2 sheets

Q: Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

A: The given equation of the surface is x2 + 2y2 + z2 - 4x + 4y - 2z + 3 = 0.The general equation,…

Q: Sketch the surfaces 1. z = y2 - 1 2. 4x2 + y2 = 36

A: Using graphing calculator to sketch themz=y^2-1

Q: Find the traces for the given surface: 16x? +16y² – 9z = 0. Then sketch and identify the surface.…

A:

Q: Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of…

A:

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x , (z = 0)…

A:

Q: Let y ==a and z =. Find the intersection of these х x2 surfaces.

A:

Q: Sketch the surfaces ASSORTED x2 + y2 = z

A: we have to sketch the surface x2 + y2 = z.

Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

A: Ellipse is a closed curve around 2 focal points such that for every point on that curve, the sum of…

Q: Identify the surface by completing the squares. x +16y² – z? – 14x + 32y + 8z = 0 O A hyperboloid of…

A:

Q: Sketch the surfaces 1.z = 1 + y2 - x2  2. z =-(x2 + y2 ) 3. 4y2 + z2 - 4x2 = 4

A: Used graphing calculator to graph:z = 1 + y^2 - x^2 from two viewing angles