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

Q: find a parametrization of the surface. 1.The surface cut from the parabolic cylinder y = x2 by the…

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Q: . Determine the area of the surface with parametric equations a = 2u?, y = v², z = 2uv, 0 <u < 3, 0…

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Q: If a parametric surface given by r₁ (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -2 ≤ u ≤ 2, -3 ≤ v ≤…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

A: Given rectangular equation is y = x2

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

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Q: parametrizes the portion of the sphere x² + y² + z² = 9 that is above the xy-plane and below the…

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Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

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Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: 2.a. Write the equation of the surface r? + y? = 4y in cylindrical coordinates. b. Classify the…

A: To convert to the cylindrical coordinates, we need to make the following substitutions: x=rcos(θ);…

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

A: We need to identify a generating curve on the xz-plane for the surface of the revolution with the…

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: Given: x2+y42+z2=1  ……1   Equation of plane is: z=14  ……2

Q: Consider the equation below. x² – y2 + z² – 4x – 2y – 4z + 7 = 0 - Reduce the equation to one of the…

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Q: Determine the characteristics of the equation z = p? -q? and find the integral surface which passes…

A: Given partial differential equation is z=p2−q2 We have to find he characteristics of the equation…

Q: Find an equation for the plane that is tangent to the surface z = In (x³ + y²) at the point…

A: Given:   A surface   z = ln x3 + y2   To Find :  An equation  for the plane that is tangent to the…

Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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Q: cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center…

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Q: Find the center C and the radius a for the spheres 2x2 + 2y2 + 2z2 + x + y + z = 9

A: General equation of a sphere, x2+y2+z2+2ux+2vy+2wz+d=0 Centre of sphere = -u, -v, -w Radius of…

Q: Consider the surface r²+y²+2ry-3x+2y-2z=1. Determine the following: (a) the general equation of the…

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Q: Find an equation in cylindrical coordinates for the surface represented by each rectangular…

A: Given  x2+y2=4z2 It can be compared with the equation of elliptic cone with its axis along z-axis.…

Q: Consider the sphere x² + y² + z² = 9. Please find the equation of the plane tangent to this sphere…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: Given:y2=10-z2r2=x2+y2x=r cosθy=r sinθz=z

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: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: The given quadratic surface is  x2+y42+z2=1 , y=0

Q: Consider the surface 4a? – y? + 2z² + 4 = 0. a. Find the value(s) of k such that the cross-section…

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Q: Sketch the quadric surface: r +4y2 +4z2 16. Note: The x, y, & z axes are depicted in red, green, &…

A: The given function is: x2+4y2+4z2=16

Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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Q: the trace of the surface in the plane x=1?

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Q: Find an equation for the surface obtained by rotating the line z = 2x about the z-axis. + x²) b. z?…

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Q: 3. Use polar coordinates to find the surface area of the paraboloid z = x² +y² – 5 that lies below…

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Q: Write the equation x +z* - (y- 1) = 0 in cylindrical sy stem. W hich surface does it represent? Give…

A: Given :            The equation x2 + z2 - (y - 1)2 = 0   To write the given equation in…

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

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Q: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…

A: We will find out the required value.

Q: Find

A: We find surface area of given region.

Q: Find the center C and the radius a for the spheres (x - 1)2 + (y - 2)2 + (z + 1)2 = 103 + 2x + 4y -…

A: Standard equation of sphere is given as x-x12+y-y12+z-z12=r2, where x1,y1,z1 is center of sphere and…

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: we have to find an equation in cylindrical coordinates for the surface represented by the…

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: p(x, y, z) = e¬x²-y²–z² +2yz

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Q: The surface x2 + y² = z² is identified as O A. Paraboloid O B. Cone O C. Hyperboloid of one sheet O…

A: the correct answer is option: D .) Hyperboloid of 2 sheets

Q: Prove that the surface of the given equation is an ellipsoid. Hence, determine its center. 9x +4y…

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Q: Plot the implicitly given surface (x − 1)² /4 + (y − 1)² +z² = 1 (a) using the sphere function. (b)…

A: As per the question we have to plot the following surface : (x-1)2/4 + (y-1)2 + z2 = 1 With the help…

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

A: Solution

Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: r2cos2θ+z2+1=0

Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Q: Consider the surface z = 4x2² + y² + 1. An equation for the tangent plane to this surface at the…

A: Given: z=4x2+y2+1

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 −…

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

A: We will identify standard  equation of type of quadratic surface by comparing   with given equation…