Find an equation for the surface consisting of all points that are equidistant from the point (0,- 3,0) and the plane y = 3. O a. x? + 12y? +z? = 1 O b. z2 +x? = - 12y Oc z2-12y =x Od. x²+y = 12z O e. z2-x = -12y

Q: Which of the following is the equation of the plane that is tangent to the surface 2 x² + y? – x z –…

A: Consider the provided information, The provided surface, 2x2+y2-xz-3z=1 Find the partial derivative…

Q: 2. Given the quadratic surface S by the equation below, determine the type of surface. 2x? + 3y? +?…

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Q: Consider the surface S: √x + √y + √z = a with a> 0. If P (x0, y0, z0) is a point on the surface that…

A: (a) The given surface S:x+y+z=a. Consider the level curve Fx,y,z=a  and a>0. Let Px0,y0,z0 is a…

Q: Match the equations of the surface with the graphs below. A D 1.9x² + 4y² + z2² = 1 2. x² - y² + z²…

A: The equations of the surfaces, 1. 9x2+4y2+z2=12. x2-y2+z2=13. -x2+y2-z2=14. x2+4y2+9z2=1

Q: The set of all points equidistant from the point (0, – 3, 0) and the plane y = 3 are represented by…

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Q: Find a parameterization for each of the following surfaces: (a) æ² + y² + z² – 4x – 6y = 12 (b) 2x²…

A: We have to find the parametric representation of the following surfaces: x2+y2+z2-4x-6y=12       →…

Q: Find the area of the cap cut from the paraboloid y + z? = 3x by the plane x = 1.

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Q: Determine the characteristics of the equation z = p? -q? and find the integral surface which passes…

A: Given partial differential equation is z=p2−q2 We have to find he characteristics of the equation…

Q: Find an equation for the plane that is tangent to the surface z = In (x³ + y²) at the point…

A: Given:   A surface   z = ln x3 + y2   To Find :  An equation  for the plane that is tangent to the…

Q: The surface S formed by the point P(x,y,z) such that the distance from P to the point A(1.0,-1) is…

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Q: Find an equation for the plane that is tangent to the surface z = In (x + y²) at the point P(0,1,0).…

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Q: Find the center C and the radius r of the sphere S :x2 +y? + z2 - 2x 4y + 4z = 16 O C (2, 4, -4) and…

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Q: When the plane x = 3 passes through the surface x2 + y? + z² = 64, %3D the curve that forms from…

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Q: Consider the surface S: Z=4x²+5y?, an equation of the plane fangent to S fhe point P(-2,1, 21) is…

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Q: 4. Let f(x, y) = V2x² – 3y². (a) What is the domain of this surface? (b) Draw three level curves of…

A: This is a problem of analysis of several variables. Contour and trace a graph.

Q: Consider the surface 4a? – y? + 2z² + 4 = 0. a. Find the value(s) of k such that the cross-section…

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Q: Find an equation for the surface consisting of all points P for which the distance from P to the…

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Q: I just need #36.

A: Given the equation

Q: Match the quadric surfaces to its graph. A. y + = 4+ 4x² C. 9z + 4y = 36 + 36z² B. 42 + y? + 4z² =…

A: We have to identify which Quadratic equation corresponds to which of the given 3D graphs.

Q: Q5) Find the equation of the surface formed by rotating the following line about the x -axis. 1=…

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Q: Find an equation for the plane that is tangent to the surface z= In (x²+y^) at the point P(0,1,0).…

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Q: 9a2 + 4y? + 36z? = 36 %3D

A: given surface 9x2+4y2+36z2=36 claim- to find the trace of given surface in planes x=k , y=k , z=k ,…

Q: Match the equation with the surface it defines. f(x, y) = -√√x²+12 X O O O stisk 3

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+4)

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

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Q: Consider the paraboloids S1 : x² + y² – 2 and S2 : 8 – x² – y?. The intersection between the…

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Q: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+ 4)

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Q: Find the extreme values of the function ƒ(x, y, z) = xy + z2 on the circle in which the plane y - x…

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Q: Let h, k, r, m, t E R. A general equation that corresponds to the above surface is: (x – h)² _ (z –…

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Q: Match the equation with the surface it defines. Also, identify each surface by type. 1. x = y? - z2;…

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Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 11x ,(z = 0)…

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Q: Sicatch the section of the surface at y-0. 2r +z = 6 AM -8-6-4 -2 -8-6 -4 -2 2 N 6

A: Here y=0 so graph is form in xz plane This is the equation of line in xz plane For x intercept we…

Q: Match the equations of the surface with the graphs below. A D 1. y=x²- z² 2. y² = x² +22² 3. y = 2x²…

A: Hyperbolic paraboloid:  y=x²-z²

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

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Q: Consider the surface S: z = 4x2 + 2y2 . An equation of the plane tangent to S at the point P (−1, 2,…

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Q: x? y? The equation of the tangent plane to the surface z? 16 -1=0 at the point (4,3, – V3) is 9. O…

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Q: Consider the surface z = 4x2 + y? + 1. An equation for the tangent plane to this surface at the…

A: Let fx,y=z. Differentiate the function f(x,y) partially with respect to x and y, to find fx and fy .…

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 =…

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Q: Let h, k, m, neR such that n > m >0. A general equation corresponding to the above surface is: A) (z…

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Q: Find an equation for the plane that is tangent to the surface z = In (x² + y) at the point P(0,1,0).…

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Q: p(x, y, z) = e¬x²-y²–z² +2yz

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Q: Find an equation of the sphere containing all surface points P = (x, y, z)  such that the distance…

A: Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance…

Q: The tangent plane to the graph of the surface z-In(x<+y) at the point (1,0,0) contains point (3,3,t)…

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Q: Which of the following represents a plane surface whose x-, y-, and z-intercepts are a, b, and c…

A: Given questions are solved.

Q: Consider the equation of the surface S given by 3x-3y®z7-2xy = 8, where a is an odd number and B is…

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Q: The tangent plane to the graph of the surface z=In(x<+y<) at the point (1,0,0) contains point…

A: and point (1,0,0)

Q: Given a sphere with center (4, 3, – 1) and radius 4. Find an equation of the intersection of this…

A: First write the equation of given sphere then satisfy the condition for intersection with xz-plane.

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

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Q: x² + 9y² – 2² = 9

A: The given equation is: x2+9y2-z2=9           (1)

Q: (3) Consider the quadric surface S C R, having equation a2 + y? - z2 = 9. Find all lines through P…

A: General equation of line from point 3,-3,3 is x,y,z=3,-3,3+tl,m,n.  Substitute it in the quadratic…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.