Consider the following equation of a quadric surface.   A. Find the intercepts with the three coordinate​ axes, when they exist. y^2/16+36z^2-x^2/9-4=0 The​ y-intercept(s) is/are

Q: Sketch the surface..........CYLINDERS............. x2 + y2 = 4

A: x2+y2=4 Now, rewrite the above surface for the function as, z=fx,y. z=fx,y=4-x2-y2

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

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Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x2 , (z =…

A: The distance of any points ( having same y co-ordinate ) on the curve is at same distance from…

Q: Find the surface are generated when y= (x^3)/5 is revolved about the x axis on the interval…

A: Explanation of the solution is given below...

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

A: Question is solved.

Q: Find the equation of the surface of revolution generated by revolving the curve z²=4y in the…

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Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: We need to determine the equation of the surface that is obtained by rotating the line z=7y about…

Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

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: 1. Consider the following equation of a quadric surface. z=x2+ 169y2 a. Find the intercepts with the…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the equation of the surface of revolution that is generated by rotating the straight line y = x…

A: The surface of revolution that is generated by rotating x=f(y) around the y-axis is x2+z2=f(y)2 so…

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

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

A: Given, z=9-x2-y2

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: Use  inertia  to  classify  the  quadric surface  given by equation. y2 − z2 − 9x − 4y + 8z − 12 = 0

A: We wish to use inertia to classify the quadric surface given by the following equation:  ------(1)…

Q: Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem…

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Q: Sketch the section of the surface at y= 0. 4. + 9 36

A: Given the equation4x2+9z2=36

Q: Describe and sketch the surface x2 + z2 = 4

A: Given- x2+z2=4 To sketch- The graph of the above function and explain it.. Concept Used- The…

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 equation of the surface of revolution of x = z2 about the x-axis.

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Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

A:

Q: Determine the projection of the following surface on the plane of the xy-axes -2y? + + =1 3 3 O…

A: -2y2+x23+z23=1To find the projection

Q: If the infinite curve y = e-2x, x 2 0, is rotated about the x-axis, find the area of the resulting…

A:

Q: 12. 4x² + 9y² + 9z² = 36

A: Given: 4x2+9y2+9z2=36

Q: Let S be the quadric with equation 36x² –4y² –9z² – 36x = 0. Sketch a graph of the surface with…

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: find an equation for the surface generated by revolving the curve about y-axis. y = 4x2, (z = 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: find the surface of both of the trainagles, all the sides *show all the work*

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

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

A: Solution-

Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x…

A: x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

Q: Sketch the surface = 2y + 32².

A:

Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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Q: Sketch the xy-trace of the sphere whose equation is (x+3)2 +(y−1)2 +(z−3)2 =18.

A:

Q: Identify and sketch the section of the surface at x = 0. 25x? + 16y² – 9z² = 0 Type of the surface:…

A: We need to sketch the section of the surface x=0, 25x2+16y2-9z2=0. For x=0, 16y2-9z2=0. The graph is…

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch on paper.…

A: Express the equation 4y2+z2-x-16y-4z+20=0 in terms of the complete squares of y and z, and then…

Q: Find the equation of the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

A:

Q: classify the quadric surface given by equation and determine its standard form.−x 2 − y2 − z2 + 4x y…

A: Given quadric Surface is         -x2-y2-z2+4xy +4xz+4yz =3 Comparing it to the general form,…

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: 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: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and…

A: To answer it, let us go through the equation of Hyperboloid of 2 sheets   x2a2 - y2b2  - z2c2 = 1…

Q: Sketch the section of the surface at x = 0. y - 252 = 25 -12- -8 12 -6 -4 -6 12 -4 -8 -12 6 4 4 -6-4…

A: topic - hyperbola y2-25z2= 25 is a hyperbola with vertex are (0,5,0) and (0,-5,0)

Q: Sketch the section of the surface at y = 0. z = 6r 4 2 -6 -4 -2 6. -4- -6 6r 4 2 -6 -4 -2- -4 4. 2.…

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Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

A:

Q: Find the equation of the line tangent to the intersection of the surface z = arctan ry with the…

A: The tangent line to a plane curve at a particular position is the straight line that "just touches"…

Q: Use  inertia  to  classify  the  quadric surface  given by equation. x2 + y2 + 2z2 − 2xy − 4xz − 4yz…

A: We have to use  inertia  to  classify  the  quadratic surface  given by equation. x2 + y2 + 2z2 −…