Identify the type of quadric surface defined by the equation +z= 1, 36 and find all x-, y-, and z-intercepts of the resulting.graph. Sketch the graph of this quadric surface on paper. The quadric surface is a / an hyperboloid of one sheet v with x-intercepts when a -6,6 y-intercepts when y -2,2 and z-intercepts when z=

Q: Show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

A: To show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

Q: Choose the equation that represents the graph of the quadric surface below 3. 21 O z = 4 - 5y2-92 O=…

A: From graph we see that the quadric surface represents a paraboloid whose axis is y-axis Here 1st…

Q: Find the center and the radius of the sphere x + y² += - 4x+ y-6z+13=0 Center: Radius:

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Q: Determine the Cartesian co-ordinates of the local maximum of the graph which is described by the…

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Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Identify the quadric surface and sketch the graph. z = x2 + 4y2

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Q: Give the maximum number of points at which the following pairs of graphs can intersect. (a) A line…

A: (a) A line and a hyperbola :The maximum number of points at which a line and a hyperbola can…

Q: Consider the parabola C: z-4 = -(x - 2)² on the rz-plane. 1. Find the center-radius form of the…

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Q: Find an equation for the surface obtained by rotating the parabola y=2 about the y-axis.

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Q: EXAMPLE 2 Describe and sketch the surface in R3 represented by the equation y = 6x.

A: Given equation : y = 6x in R3

Q: Determine the equation of the parabola with the directrix z = 3 and focus (0, 7). O y = 8 (z – 5) O…

A:

Q: Find the quadratic surface and sketch the graph of r+y +- 4xyz = 1

A: The given equation is: x2+y2+z2-4xyz=1

Q: identify the surface defined by the equation and match it to the appropriate graph

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Q: Find the equation of a sphere whose center is on line 5y+2z=0=2x-3y and passes through point…

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Q: Identify the type of surface represented by the given equation.

A: Since we are given x25+y28-z22=1 -(i) and for finding the nature of surfacewe will solve for z.

Q: The graph of x2+y2+z2-14y=0 is a sphere. what are the center and radius of the sphere?

A: Given    Equation of sphere  x2+y2+z2-14y=0To calculate:-     Center  and  radius  of the sphere.

Q: Identify the surface whose equation is given.

A: ρ cos Φ =1  -> z = 1 ( as we know in spherical coordinates z = ρ cosΦ)

Q: Identify the surface that corresponds to the equation 3y^2 - 2x - 8z^2 = 0. O elliptic hyperboloid…

A:

Q: 17. Find an equation in standard form for the circle centered at (7,–2) with radius 8. A. (x – 7)² +…

A: I have appended the formula used in the solution part.

Q: 5. Find the standard form equation of a sphere that has a diameter with endpoints (3, -2, 4) and (7,…

A: Given : The end points of a diameter of a sphere are  (3, -2, 4) and (7, 1, 4). To find : We have to…

Q: Reduce the equation to one of the standard forms, classsify the surface,and sketch it. x2 - y2 - 4x…

A: Given : equation x2-y2-4x-2z+3=0To find : reduce the equation in standard form, classify the surface…

Q: Identify the quadric surface each of the following equations represent and sketch its graph in a…

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Q: Choose the equation that represents the *graph of the quadric surface below

A: Given,

Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: Given a cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of…

Q: A hyperbola is the set of points in a plane, the difference of whose distances from two fixed points…

A: Given : A hyperbola is the set of points in a plane the difference of whose distances from two fixed…

Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: 9. Identify the center and radius of a circle with equation (x-7) +(y+6) = 16. Ocenter at (7,-6);…

A: Given problems:-

Q: Find the surface of the regular pyramid.

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Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. O elliptic…

A: To identify the surface that corresponds to given equation- 100y2-25x2-4z2=1.

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: Identify and sketch the section of the surface at x = 0. Туре: hyperboloid of one sheet 4 elliptic…

A: We are given: x2+y29+z225=1 We need to sketch the graph of the surface at x=0. This can be done as…

Q: A surface in space is defined by the equation -4x? + 16y- 8z2 = 0. Which one of these is true? O The…

A:

Q: Find an equation of the sphere with center (-3, 2,5) and radius 4. What is the intersection of this…

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Q: Is the set of all points in a plane, the difference of whose distances from two fixed points (the…

A: For the given statement

Q: II. Solve the following. Slems. 1. 2. Name and sketch the graph of the surface with equation +z2 –÷=…

A: Given

Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 ,…

A: \ Revolution of the hyperbola about its transverse axis generates a surface of two sheets, two…

Q: Identify and sketch the surface -25x^2 +4y^2-100z^2=100.

A:

Q: Choose the equation that represents the graph of the quadric surface below 3 O y = 4 – 5x² – 922 O I…

A: We have given a quadric surface. It is asked to find the equation of the surface from the given…

Q: What are the intersections of the conic section formed by the points A(0,1),B(2,3),C(5,4),D(1,…

A: Below are graph and input view.

Q: Identify and sketch manually the graph of the quadric surface 25x² -25y² -9z²-150x + 200 = 0.

A: Solution :-

Q: Rewrite the given equation of a quadratic surface and identify the graph. 12y2 – 3z2 = 16x

A: equation of the hyperbolic paraboloid  A y2 - B z2 = 2 Cx

Q: Show that the envelope of the family of circles whose diameters are the double ordinates of the…

A:

Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1.* O elliptic…

A: The various types of quadric surfaces are: the ellipsoid, the hyperbolic paraboloid, the elliptic…

Q: Identify and sketch the graph of the quadratic surface 4x2-y2-z=1

A:

Q: Identify the surface generated by the equation 9y^2 + 4x^2 - z^2 = 36 hyperboloid of 1 sheet,…

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Q: Match the quadric surface with the a plausible equation for the graph by drawing an arrow from the…

A: The objective is to match the surface with equation for graph and then by its name.

Q: The surface of equation – +- 1 is: 16 A sphere O A cone O An ellipsoid || + 이닙

A: We can explain it as below using the concept of three dimensional geometry.

Q: Identify the quadric surface each of the following equations represent and sketch its graph in a…

A: Let's find.

Q: Identify the quadric surface as an ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets,…

A: Here is the solution of the given problem.