Q1 Find extrema point of the Surface 2-ペ-S-12x+3}+2

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

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Q: Identify and sketch the surfaces y = - (x2 + z2)

A: Given Data The equation of curve surface is y=-(x²+z²)   The sketch of the surface equation is,

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: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

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

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

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Q: 5. Use traces to sketch and identify the surface x2- y? - z2 = 4.

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Q: Using elimination method, find the minimum distance from the curve y=2-x2 to the origin.…

A: To find minimum distance from the curve y=2-x2 to the origin  Let us consider the Lagrangian…

Q: Describe and sketch the surface (x2/16) + (y2/9) + z2 = 1

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Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by…

A: As per the instruction, we will be answering the first question. Given: We need to find the volume…

Q: Identify the surface y − 3 = x² +.

A: Solution: Given data, y - 3 = x2 + z2

Q: Q3: Find the points on the surface x^2+z^2-6=0, closest to the origin.

A: The distance of the point on the surface is given by d=x2+y2+z2. To obtain the distance insert the…

Q: Classify and sketch the surface 4x2 − 3y2 + 12z2 + 12 = 0.

A: Solution:Given surface4x2 - 3y2 + 12z2 + 12 = 0    — 1divide equation 1 with -12,⇒ x2-3 + y2u - z2 -…

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

A: Given surface is x2+z2=y2. The given equation is in the form of x2a2+z2c2=y2. So, the given surface…

Q: Q3: Find the points on the surface x^2+z^2-630, closest to the origin.

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Q: Identify and sketch the surfaces x2 + (y - 1)2 + z2 = 1

A: given: the equation of the surface x2+y-12+z2=1

Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Find the area of the surface x^2-2y-2z =0 that lies above the triangle bounded by the lines x=2,y=0…

A: From the given equation. 2z=x2-2yz=x2-2y2z=x22-ydzdx=x, dzdy=-1 From the limits x limits from 0 to 2…

Q: Sketch the surfaces 1. x2 + y2 = 4  2. x2 + 4z2 = 16

A: The given surfaces are sketched using online 3D calculator.

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: Find the slopes of the surface in the x- and y-directions at the given point.

A: z=25-x2-y2, 3, 0, 4 Partially differentiating with respect to x, we get ∂z∂x=1225-x2-y2·∂25-x2-y2∂x…

Q: Q3: Find the points on the surface x^2+z^2-2=0, closest to the origin.

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Q: Sketch the surface x = 2y2 +3z2

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Q: Identify and sketch the surfaces z = - (x2 + y2)

A: Identify and sketch the surfaces z = - (x2 + y2)

Q: Parameterize the line of intersection of the surfaces: x2 - y2 = z - 1 and  x2 + y2 = 4

A: Given equations of surfaces are: Rewriting the second equation:

Q: 12. 4x² + 9y² + 9z² = 36

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

Q: draw vertical and horizontal traces to identify the surface y = x^2 + 9z^2

A: The graph of the given surface is

Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: Find the length of the curve 3x = (y² + 2)³/2 from y = 2 to y = 3 %3D

A: Use length of curve formula:-  for a given curve x = f(y) from y=y1 to y=y2 length of curve,…

Q: 4. Parameterize the curve of intersection of the surfaces z = x² + y² and y² + (z – 1)² = 1.

A: parameterisation

Q: (a) Find the area of the surface generated by the given curve about x-axis y = V, (b) Find the area…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  y = Square root…

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Q: Plot the surface of 6a2- 2x4- y?z2 = 0, for -10 <x, y, z < 10

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Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: Find the slope of the surface z = 3x/y at the point (5,2,15/2) in the x- and y- directions.

A: Given data is: z=3xy  To find the slope of the surface z at the point 5,2,152 in the x and…

Q: Describe and sketch the surface 16x2 + 16y2 − 9z2 = 0

A: Given surface 16x2+16y2-9z2=0

Q: The slope of the surface z = xy2 in the x-direction at the point (2,3) is ______, and the slope of…

A: Given, surface, z = xy2Differentiating the z with respect to x assuming y as constant,∂z∂x = y2×1 =…

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 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: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

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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: Q1/ Use traces to sketch and identify the surface z2 - 4x2 - y² = 4

A: Let's find.

Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Q: Cone: x2 + y2 - z2 = 0, Plane: x + 2z = 4

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.