• Consider the surface given by the equation (r- 1)² + (y+3)2 - (z-2)² = 1. Which of the following are its y-intercepts? a. 1 and 5 b. -1 and -5 c. 2 and 4 d. -2 and -4 а. b. O d.

Q: Identify the surface defined by the following equation. 2x-y²-z² =0

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Q: Which one of the following is a set of symmetric equations for the line normal to the surface given…

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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: Let (P) be the surface of equation 2x+4y² =16 and (Q) be the surface of equation x=-1-3y²-3-². Then…

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Q: Reduce the following given equation to a canonical form quadratic surface by performing suitable…

A: The given equation is, x2+y2+z2+4xy-4xz+4yz-2x+y-3z=0

Q: identify the following quadric surface x^2/6 + y^2/6 + z^2/16 =1

A: This question is related to Quadric surfaces, we will solve it using given information.

Q: Identify and sketch the section of the surface at x = 0. 25x + 4y? – 16z = 0 %3D Type of the…

A: Question is solved.

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given: The equation of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

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: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: The r- intercept of the surface 2r2 + 6y² – 3:² = 8 is equal to c.(+2, 0, 0) d. (±3, 0,0)…

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Q: What is the name of the surface defined by the equation y? x? + + 2z? = 1?

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Q: Identify the quadric surface satisfying each of the given equations and then make a rough sketch to…

A: identify the quadric surface satsifying each of the given equations and make rough sketch to show…

Q: Match the equations of the surface with the graphs below. D 1. z2 + 4y? + 922 = 1 |2. z2 – y? +22 =…

A: We need to match graphs.

Q: When the plane x = 3 passes through the surface x² + y? + 2? = 64, the curve that forms from…

A: Given, the plane x = 3 passes through the surface x2 + y2 + z2 = 64 . The intersection of plane x =…

Q: Find the slopes of the surface in the x- and y-directions at the given point. h(x, y) = x2 − y2 (-2,…

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Q: Identify and sketch the surfaces x2 + z2 = y2

A: Given surface is x2+z2=y2. The given equation is in the form of x2a2+z2c2=y2. So, the given surface…

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

A: Given: x42+y82+z122=1

Q: Identify and sketch the section of the surface at x = 0. 2y? – x + 22 = 50 Type of the surface:

A: This question is related to conic section .solve in step 2.

Q: Given the expression x⁴-3x+7=y³ on the interval [3,5], determine the surface of revolution if it is…

A: Given that, the expression is x4-3x+7=y3.

Q: 11. What is the equation of the surface revolved about the x-axis for 2² - xz = ln x + 3x? A. y²…

A: Introduction: When a surface is revolved around the coordinate axis, another surface is obtained. In…

Q: - The surface 5x^2 + 2z^2 = 3y is heading towards which axis? - Identify the surface generated by…

A: 5x^2 + 2z^2 = 3y x= 3n1 ,  y = -3(5n12 + 2n22) , z = 3n2

Q: What is the name of the surface defined by the equation -y? + x? = 1?

A: We have to find surface name defined by the equation -y2-z22+x2=1

Q: Which of the following represents the equation of the surfaces with the following four views? Freet…

A: To find which of the following represents the equation of the surfaces with the given four views.

Q: Name the surface and graph the given equations in R’: . z+x = 1 b. 2x+3y = 6 с. у%3Dsin x d. z =1- y…

A: (d) Given z=1-y2 we write it as y2=1-z This is the equation of a parabola. For plotting it, we make…

Q: Identify the equation associated with each graphed surface. (a) O z? – 1 = y? + 2? O 22 + y² = z O…

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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: Sketch the following surfaces. (a) −9z2 −5y2 −x+4 = 0 (b) 4y2 + 9z2 − x2 = 0 (c) 1−3z2 −y2 −4x2 = 0

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

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Q: x = z? + y? Name of the surface

A: x=z2+y2 We need to name the surface.

Q: Identify and sketch the section of the surface at x = 0. + 4 Туре: 61 6F 6r 4 41 2 4 6 8 -6 -4 -6 -4…

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Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

Q: Sketch the surface in R' of the equation presented. x2 + y? - 8x = 0

A: Sketch the graph on xy-plane, i.e., when z=0

Q: Describe the surface given by the equation, and find xy-trace, xz- trace, and yz-trace. 16x2 + 16y?…

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Q: Find the equation of the plane that passes through the point (2, 1,2) and is tangent to the surface…

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Q: Match the equations of the surface with the graphs below. A в D E F 1. 9a? + 4y? + z² = 1 2. a2 +…

A: now identifying the given quadratic surface

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

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Q: Identify and sketch the surface r+y +- 2r +2 = 0.

A: Answer

Q: Consider the following equations of quadric surfaces: b) x² – y² + z? = 4 i) Identify the type of…

A: Given equation of quadratic surfaces:                        x2-y2+z2=4

Q: Which of the following is an equation of a plane surface? O 2x +3y + 4z = 4 O 2x2 +3y + 4z = 4 O 2x…

A: To find:- Select an equation of plane surfacefrom given options

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

A: Given the surface

Q: (y – 3)² - Consider the surface T with equation 4 + 22 = 1. 3

A: Curve sketching (or curve tracing) is a technique used in geometry to get a general impression of…

Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

Q: Sketch the surface given by the function. z= 9-x?-y? 2x -2 2x

A: Answer

Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

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Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: Given surface, gx,y=4-x2-y2 and point 1,1,2

Q: 15) Consider the following equations of quadric surfaces: a) x = + - 4 b) x? - y? + z? = 4 i)…

A: We need to find surface type and intercepts.

Q: The surface given by z = x² – y? is cut by the plane given by y = 3x, producing a curve in the…

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Q: x² + 9y² – 2² = 9

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