Describe the 3-D surfaces in words and draw a graph. Your description should include the shape, location, and direction/orientation. a. y = x b. (x – 1)2 + (z – 1)2 = 4 c. y = z2

Q: Q3: Find the points on the surface x^2+z^2-5=D0, closest to the origin.

A: see the attachment

Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

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Q: Describe the surface whose equation is x2 + y? + z2 + 6x + 8y + 8z – -16 = 0. Surface description:…

A: Given:- x2+y2+z2 +6x+8y+8z--16=  To find:- Surface description

Q: Analyze the trace when the surface z = (1/2)x2 + (1/4) y2 is intersected by the indicated planes.…

A: Consider the value of y=4

Q: Describe the surface with equation x² + y? + z? + 8x + 4y + 2z – 4 = 0) The surface is a sphere with…

A: Topic:-  sphere equation

Q: Consider the following equation of a quadric surface. y? x2 225 225 a. Find the intercepts with the…

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Q: Match the equation with the surface it defines:

A: given equation is x24+y24=z249

Q: y? Assume you are given the surface S with equation p2 9. 1.

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Q: Sketch the section of the surface at x = 0. y? - 25z? = 25 12 -12 -8 12 -4 -8 -12 4 -6 -2 -4 4.

A: topic - hyperbola

Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹ x² + y² O 3 4 y x

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Q: d. x+ z = 5

A: Given the equation of surface is : x+z=5

Q: 3. 4x+y 4

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Q: Let h, k, r, m, n be constant and m, n> 0. A possible graphical representation for the surface of (y…

A: Given Equation:      r-z -y-k2n2 = x-h2m2

Q: Sketch the given surface (x/4)^2 + (y/8)^2 + (z/12)^2= 1

A: Given: x42+y82+z122=1

Q: Describe the surface in three-dimensional space given by the equation x2+ y2+ z2 -8z=9 O a. A sphere…

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Q: 13. Consider the equation: 4x² +9z? = 36 Describe the traces. а. b. Describe the rulings. с. Sketch…

A: Here is the solution of the given problem.

Q: Given  z=44−27x2  is a curve in the xz-plane. If the equation of the surface generated by revolving…

A: Given  z=44−27x2 is a curve in the xz-plane. The equation of the surface generated by revolving the…

Q: Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface…

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Q: Consider the following equation of a quadric surface. a. Find the intercepts with the three…

A: Let a three variable equation fx,y,z=01 x - intercepts when y=0=z2 y - intercepts when x=0=z3 z -…

Q: a) Sketch the graph of the surface z = 5 – x2 – 3y?. b) Sketch the graph of z = 2.

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Q: Consider the following equation of a quadric surface. 400 400 a. Find the intercepts with the three…

A: The given equation of a quadratic surface                   y2400-x2400=z ⋯⋯⋯⋯⋯ (1) To find     The…

Q: Describe the shape of the surface: x? + y2 = 9. How would you describe the curve of the intersection…

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Q: Consider the surface in 3D described by the equation z = x² + y? – 16. (You might want to start by…

A: We are given that z=x2+y2-16 which is an Elliptical Paraboloid. We have to describe the trace in xy…

Q: (a) What does the equation x² + y´ = 1 represent as a curve in R? (b) What does it represent as a…

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Q: 1. 2. 3. 4. 5. 6. Match the equation to the graph of the surface. 1. z = x² + y

A: The given equation is z=x2+y2 This will form a 3D graph as there are 3 variables

Q: Consider the following equation of a quadric surface. x= 9- 9y? - z? a. Find the intercepts with the…

A: We are given: x=9-9y2-z2For x-Intercept : y=z=0⇒x=9 is the x-intercept.For y-Intercept :…

Q: Sketch the graphs of the following surfaces in R3 A) z^2=y^2+x^2 B)z=y^3

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Q: 5) Classify the surfaces, listing shape, location, and orientation: a. 4(x-1)2 + 9y+1)² + z² = 36…

A: Given:  4(x-1)2+9(y+1)2+z2=36 ⇒4(x-1)236+9(y+1)236+z236=1⇒(x-1)29+(y+1)24+z236=1 This is of the form…

Q: Identify and sketch the section of the surface at x = 0. 2y? - x + 2z = 32 %3D Type of the surface:…

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Q: Consider the equation 4x² - 3y² + 12z² = -12. Describe the traces of this surface on the xy-plane,…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Write an equation for the level surface of f(x, y, z) = r² + 10y? + 20z2 corresponding to the level…

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Q: Answer the question below: 1.) The student task is to find an equation of the level of surface of…

A: We want to find the equation of the level surface.

Q: Identify the following surfaces and sketch your graphic: A)4x² + y²-2y+9Z-35=0 B)y² + 4z² =x

A: Quadric Surface: A graph of a function of two variables z=fx, y is called a quadric surface. There…

Q: Consider the following equation of a quadric surface. x y 49 + 324 a. Find the intercepts with the…

A: Answer

Q: Consider the following equation of a quadric surface. 4x? + 16y? + 16z? = 64 a. Find the intercepts…

A: The graph of the given surface is given as follows :

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

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Q: Consider the following equation of a quadric surface. y? z? =D1 25 2 - 25 25 a. Find the intercepts…

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Q: = V16 – x², -2<x<3, is rotated about the x-axis. Find the area of the resulting surface.

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Q: A possible graphical representation for the surface of equation (y -k)? +B(x-h) = 0, with B > 0, is:…

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Q: Consider the following equation of a quadric surface. x2-y² +z2 - 4 = 0 a. Find the intercepts with…

A: The equation of a quadratic surface                                                 -x2-y2+z2-4=0…

Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² + y²

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Q: ) Classify the equations below as one of the following types of surfaces: A. parabolic cylinder, B.…

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Q: Consider the equation below. x2 - y2 + z2 - 4x - 2y – 2z + 4 = 0 Reduce the equation to one of the…

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Q: Identify and sketch the section of the surface at x = 0. 1 Туре: 61 61 61 61 4. 4 4. 4- 2 -8 -6 -4 4…

A: Let's find.

Q: Name the surface and draw an accurate Graph of y = x² + z² in R'.

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Q: What are the z-traces of the surface x2+ y2+ z=5? O a. Circles. O b. Ellipses. O. Hyperbolas. O d.…

A: here we have to find z- traces and x- traces of the given equation.

Q: raph and identify the shape of the following surfaces given by the following equation (as well as…

A: The equation is x29+y225+z24=1

Q: Identify the following surfaces and sketch your graphic: A)4x² + y²-2y+9Z2-35=0 B)y² + 4z² =x

A: We will standardize  given equations 1st and then find required surface ,

Q: ZA z = 1/x y = 1/x z = y/x yz = 1

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Q: nsider the equation of the surface S given by 2x. + 3XYP + y2 wher mber and ß is an impair number ,…

A: In this question, the concept of the derivative is applied to find out the tangent to the plane.…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.