Sketch the surfaces 1. . z = x2 + 4y2  2. x = 4 - 4y2 - z2 3. x2 + y2 = z2

Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

A:

Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9

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

A: We need to find the equation of the surface. Please find step by step solution below:

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

A:

Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: We need to determine the equation of the surface that is obtained by rotating the line z=7y about…

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given: The equation of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

Q: 5. Plot the surface of 6x2 – 2.r – y?z2 = 0, for -10 <r, y, z < 10 %3D | |

A: To plot the given surface.

Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: Consider the normal line to the surface z = x2 + y² (paraboloid) at the point P(1, 1, 2). Find the…

A:

Q: Let y= - Find the intersection of these surfaces, Calculate the GB of wrt lex order x>4>2)

A:

Q: Suppose that an equation for the surface is S(x,y) = xye^x. In what direction (relative to the…

A:

Q: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

Q: Sketch the surface: x + 2y + 3z = 12.

A: First find the intersection of plane with axis then draw the plane.

Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

A:

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

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

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

Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

A:

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: Sketch the section of the surface at y = 0. 1 + x² + y² Z = 4 -8 -6 -4 -2 4 4 6. 4 -8 -6 -4 -2 2. 4…

A: Given data is: To sketch the surface at y=0 z=1+x2+y2

Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: Sketch the surface r = 2y? + 32².

A:

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

A:

Q: Evaluate F dS, S where 4 F(x, y, z) = (3y, -2x, -), and S is the surface that is composed of the…

A:

Q: Sketch the section of the surface at y=0. z = /2+x² + y?

A:

Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

A:

Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: Let f(x,y)=/4– 4x² – y² . Find its domain and give a rough sketch of its surface.

A: The given function is:fx, y=4-4x2-y2To find domain and sketch the surface

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given:- The equation of the surface revolved for the x-axis is, z2-xz=ln(x)+3x

Q: Show that the surfaces x2 + 2y2 + 3z2 = 3,   x2 + y2 + z2 + 6x − 10y + 14 = 0, are tangent to each…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: We have to solve given problem:

Q: Let S be the surface given by the equation x^3+y^3-xz=5. What is the equation of the tangent plane…

A:

Q: What are the reace curves of this surface for x=0, y=0, and for z=k? Name the shape of the surface.…

A: Note : In the question it has to be '' trace curves '' instead of '' reace curves ''. So, we are…

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

A: Express the equation 4y2+z2-x-16y-4z+20=0 in terms of the complete squares of y and z, and then…

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: Sketch the surface z = f(x,y). f(x.y) = 4x2 + 4y2 + 2 O A. OB. OC. OD. N

A:

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: Sketch the section of the surface at y = 0. z = V4 +x² + y? 6 6 -8 -6 -4 -2 -2 -5-4-3--1, -8 -6 -4…

A: Given query is to the graph of the given expression.

Q: Sketch the surfaces 1. z = y2 - 1 2. 4x2 + y2 = 36

A: Using graphing calculator to sketch themz=y^2-1

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

A: Solution

Q: Identify and sketch the section of the surface at z = 0. v2 = 1 25 4 16 Type of the surface: too 4 4…

A: Solve the given

Q: Sketch the section of the surface at y = 0. z = 6r 4 2 -6 -4 -2 6. -4- -6 6r 4 2 -6 -4 -2- -4 4. 2.…

A:

Q: The surface that is linear with the three variables, x, y, and z is called cylinder plane sphere O…

A:

Q: Evaluate Sſ Ands where A= (x+y*)î – 4xj +4yzk and s is the surface of the plane, 2x+y+2z=8 in the…

A:

Q: Sketch the surfaces ASSORTED x2 + y2 = z

A: we have to sketch the surface x2 + y2 = z.

Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

A: Ellipse is a closed curve around 2 focal points such that for every point on that curve, the sum of…

Q: Sketch the surfaces 1.z = 1 + y2 - x2  2. z =-(x2 + y2 ) 3. 4y2 + z2 - 4x2 = 4

A: Used graphing calculator to graph:z = 1 + y^2 - x^2 from two viewing angles

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.