State the type of the quadratic surface: (종)? - (3)2 + (주)2 D1 1. Ellipsoid 2. Hyperboloid of one sheet 3. Hyperboloid of two sheets 4. None of these Describe the trace obtained by intersecting with the plane z = 1: 1. Ellipse 2. Hyperbola 3. Circle 4. Empty set

Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: Identify the surface defined by the following equation. 25x? +y? = 4 The surface defined by the…

A: Answer

Q: Consider the following. 3x + 3y + 7z = 63 Sketch a graph of the plane.

A: 3x+3y+7z=63 x intercept = (21,0,0) 3x+3*0+7*0=63 3x=63 x=21 y intercept = (0, 21,0) 3*0+3*y+7*0=63…

Q: State the type of the quadratic surface: ()' - (5)' + (¿)° = 1 2 1. Ellipsoid 2. Hyperboloid of one…

A: Here we need to find the type of quadratic surface and it's trace obtained by the plane z=1

Q: The quadric surface, * - a - = 1 l is a hyperboloid %3D 64 None of these of one sheet that opens…

A: The given quadratic surface is: x24-y264-z216=1

Q: A radio telescope has a parabolic surface. If it is 9 m deep and 12 m wide, how far is the focus…

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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: Match the equation with the surface it defines:

A: given equation is x24+y24=z249

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

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Q: Find the equation of the xy-trace of the sphere. (x – 2)? + (y + 4)² + (z – 6)? = 72 Sketch the…

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Q: A cooling tower, such as the one shown in the figure, is a hyperbolic structure. Suppose its base…

A: Let the tower be a hyperbola centered at the origin as shown in the figure. Since the lowest…

Q: Find the center and the radius of the sphere. x2+y2+z2+4x-5z=0

A: Comparing with standard equations of sphere,

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

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Q: By setting one variable constant, find a plane that intersects the graph of z=9x^2−3y^2+1 in a:…

A: Given that -  z=9x^2−3y^2+1

Q: State the type of the quadratic surface: (중)"- (1)" + (주)'=1 1. Ellipsoid 2. Hyperboloid of one…

A: NOTE: Refresh your page if you can't see any equations. . here two of the variables have positive…

Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: Sketch and identify the surface given by the equation Z=: x² +

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Q: 1. (a.) Name the given quadric surface and give its axis (c.) Name its trace on y = 2. 45x² + 20y +…

A: Given : An equation 45x2+20y2+36z=0 To find: a) Name of given quadratic surface              b)…

Q: Identify the type of surface (in space) given by the equation, and sketch the surface. a. x^2+y^2=25

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

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

A:

Q: Consider the two ellipses in the x y plane given by the equations (x-1)2 2 =1 and (x+2)2 (y-5)2 62…

A: Given:  The given ellipse equations are x-1262+y232=1and x+2222+y-5242=1

Q: The Cassegrain telescope design (dating back to 1672) makes use of the reflective properties of both…

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Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z=2 and the…

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Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

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Q: Write the equation for the surface generated by the revolving curve y = 2x +1, revolved around the x…

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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: 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: Identify the type of surface represented by the given equation. x? ? z? 10 =D1 7 O Elliptical cone O…

A: Given query is to find the surface represented by given equation.

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 coordinates of the four points at which the hyperboloid of one sheet given by x2 y? + 16 z?…

A: This question is related to 3D coordinate geometry, We will solve it using given information.

Q: Which of the following quadric surfaces most resembles a football or rugby ball? Select one: O a.…

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Q: Consider the equation 4y^2 + z^2 − 4x − 8y + 4z + 8 = 0. Then classify the surface it represents…

A: Given equation of surfaces 4y2+z2-4x-8y+4z+8=0

Q: Find the equation of the surface of revolution that is generated by rotating the parabola y = x^2…

A: Equation of surface of revolution of a curve about y-axis is given by x2+z2=r2 where r is the radius…

Q: Identify the quadratic surface, explain the shape and describe the traces. 1. a) z = -sqrt…

A: Identify the quadratic surface,Explain the shape and describe the traces.a) z=-2-x2-y2b) x2+z22=1c)…

Q: Find the standard equation of the sphere with the given characteristics - Center: (3, −2, 6);…

A: We have to find the standard equation of the sphere where, center is given as 3, -2, 6 and radius is…

Q: Sketch the graph of the equation in xyz coordinate system and identify the surface 8x? + 4y? – z2 =…

A: Sketch the graph for the given surface.

Q: Reduce the equation to standard form, classify the surface and sketch it    4y2 + z2 - x - 16y - 4z…

A: Given: 4y2 + z2 - x - 16y - 4z + 20 = 0

Q: Find the equation of the surface of revolution generated by rotating the parabola y = z^2 around the…

A: A surface of revolution generated by rotating a curve described by y=f(z) around z-axis is given as…

Q: Simplify and identify the quadric surface, given: 9x2 – 18x + 4y² + 16y – 36z + 25 = 0

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Q: Sketch the surface in R' of the equation presented. 4x² + y? = 36 Interactive 3D Graph - 10…

A: The given equation is, 4x2+y2=36x29+y236=1x232+y262=1⋯⋯1 In 2D, equation (1) is a equation of a…

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: Express the following equations in standard form to name the corresponding surface and sketch a. x²…

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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: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

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

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Q: Which of the following best describes the surface represented by the equation -- =1? cylindrical…

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Q: Consider the following equation of a quadric surface. 9x2 + 4y? + 4z? = a. Find the intercepts with…

A: Question is solved.

Q: The interior of a satellite TV antenna is a dish having the shape of a (finite) paraboloid that has…

A: Given, The interior of a satellite TV antenna is a dish having the shape of a (finite) paraboloid…

Q: 32. Which of the following is the trace of the surface in the plane y=3? Hyperbola Ellipse Parabola

A: Consider the given surface as 9x2+z2-3y=0

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.