Graph the quadric surfaces given by the equations in Exer- cises 41–48. y2 41. x² = y? x2 42. z2 9. - 25 43. x? + y² + 1 =z² 44. x? + y? – z² = 1 x2 y? 45. z= - + 25 9. 46. 9x2 + 16y² + 16z² = 144 %3D 47. z = x2 – y? 48. z = x² + y² + +

Q: Explain why the curve of intersection of the surfaces x + 3y? – 2z2 + 2y = 4 and 2x? + 6y? – 4z2 –…

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Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…

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Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Identify and sketch the surfaces 4x2 + 4y2 + z2 = 4

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Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: 3. Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x -6y + 2z = 5.

A: Given equation of planes: 2x-3y+z=4 and 4x-6y+2z=5. To find: Shortest distance between the parallel…

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: Sketch the surfaces ASSORTED 4y2 + z2 - 4x2 = 4

A: Given:  And can be written as,  Therefore, The obtained function is in the form of Hyperboloid…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: What is the shortest distance from the surface xy + 15x + z2 = 204 to the origin? distance =

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Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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

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Q: The first car A moves in the northern direction at a speed u(mph), and the second car B moves to the…

A: The first car A moves in northern direction i.e. towards positive y-axis and the second car B moves…

Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

Q: If a bug walks on the sphere x^2 + y^2 + z^2 − 4x + 4y + 4z + 3 = 0 how close and how far can it get…

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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: Find and classify all the critical points of the surface with its equation z = 3x"y + y* – 3x2 – 3y?…

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Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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Q: B) Determine the parametrizations of the untrimmed surfaces S1, S2 and S3 without constraints(free)…

A: Given: Surfaces S1: 2x-4y+z=4 S2: 2y=6-x S3: x2=16-4z To find: Parametrization of the surfaces S1,…

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of…

A: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of the…

Q: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

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

A: Given surface equation is

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

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Q: (a) Where does the normal line to the ellipse x2- x   y + y 2 = 3 at the point (1, -1) intersect the…

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Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

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

A: The objective of the question is sketch the section of the surface at y=0.

Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

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Q: 1. Trapezoid JKLM with vertices J(-6, 6). K(-3,7), L(-1.3), and M-8, 0): (x, y) (x+7, y-3) J'() K'…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find the minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

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Q: Find and classify all the critical points of the surface with its equation 2 = 3a²y + y3 – 3x² – 3y?…

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Q: Find the point on the sphere x²+y²+z²=4489 that is farthest from the point (18,-20,18).

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Q: ind the equation of the parabora y= ax^2 +bx +c that passes through points (0,3) (1,-4) (-1,4)

A: Consider the equation of parabola is given as in the question and passing through the points (0, 3)…

Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

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Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below