(3) Consider the quadric surface SC R, having equation a2 + y? – 22 = 9. Find all lines through P = (3,-3, 3) that lie entirely on S or show that no such lines exist at all.

Q: Consider the rormal line to the surface z= z + y? (parabokoid) at the point P(1,1, 2) Find the point…

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Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

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

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Q: Suppose we have a quadric surface described by 1 (r, y, z) | 1 1 = 7. 1 -4 Using canonical…

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Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: Evaluate the surface SS₂ xz ds S is the part of the 2x+2y+z=4 that li- the first octant.

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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: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

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Q: At what points does the curve r(t)=(t,t,14t) intersect the surface z=x2+3y2?

A: Given: rt=t,t,14t, z=x2+3y2 for finding intersection point of curve and surface we put point t,t,14t…

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: Consider the surface given by the equation z – y = x². Draw a total of at least 3 traces in at least…

A: It can be solved in 2nd part using simple geometry.

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: 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 surface z = (x+ 1)² + (y – 2)² – 1 - Select a correct name for this surface and point…

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Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: a) Evaluate x²y? ds, where the curve C is the intersection between the surface z = := V1– y? and the…

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Q: Find the points on the surface x2 - zy = 4 closest to the origin.

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

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Q: 1. Consider the following equation of a quadric surface. z=x2+ 169y2 a. Find the intercepts with the…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

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

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Q: The attached figure shows the surface S1: y + z= 2, limited in the first octant with surface S2: x =…

A: The area of a surface z=f(x,y) bounded by the region R is given by the integral expression:-…

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: Consider the surface S: Z=4x²+5y?, an equation of the plane fangent to S fhe point P(-2,1, 21) is…

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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: 3. Consider Hhe following two surfaces. 8x-54-82 = -13 a) Show that the surdaces intersect at the…

A: Given surfaces are  z=2 xy2 and 8x2-5y2-8z=-13 (a)  Let fx,y,z=z-2 xy2=0 Let gx,y,z=8x2-5y2-8z+13=0…

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

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Q: If the maximum distance from the surface x? + 2y² + z? = 3 to the point (1,0, –1) is Va+ bv6, what…

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Q: Let (P) be the surface given by the following equation z = 5-x²-y² and (Q) be the surface given by…

A: Given surface P is, z=5-x2-y2    ----(1) For xy projection, put z=0 in (1) we get, 0=5-x2-y2⇒…

Q: Find a generating curve and the axis of revolution for the surface                             x2 +…

A: Find a generating curve and the axis of revolution for the surface   x2+3y2+z2 =9 If the equation of…

Q: The surface 22 = x² +y? – 4x + 5 remains unchanged when rotated about the line L in R³ Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

Q: a) Evaluate y° ds, where the curve C is the intersection between the surface z and the plane x = 3…

A: Integration problem...

Q: The surface z? = x² + y? – 4x + 5 remains unchanged when rotated about the line L in R Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

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: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-1).

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Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

Q: Consider the surface x² - y² + z² = −4. A. Identify the name of the surface. B. The line…

A: We know general form of hyperboloid of two sheets is  -x2a2-y2b2+z2c2=1 where positive term is the…

Q: The part of the surface z =1  + 3x+ 2y 2 that lies above the triangle with vertices (0, 0), (0, 1)…

A: Part of the surface: z=1+3x+2y2∂z∂x=3, ∂z∂y=4yVertices of the triangles are (0,0) , (0,1) , (2,1)

Q: If a parametric surface given by ri (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -3 <u < 3, –4 < v<…

A: We solve this

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

Q: Given the surface z = In(-2x² + 5y² – xy). Find the equation of the tangent plane and the parametric…

A: Surface given z=ln(-2x2+5y2-xy) Point P4,3,0

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

A: Curve sketching (or curve tracing) is a technique used in geometry to get a general impression of…

Q: Which of the following is a defining equation for the tangential plane to the surface defined by…

A: To find  An equation for the tangential plane to the surface defined at the point (1, 1,1)

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

A: Solution

Q: Consider the surface given by the equation z - y = x2. Draw a total of at least 3 traces in at least…

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Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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Q: 4. Consider the equation 16y" - 4 + 2² = 16. By first deseribing all of its traces, sketch the…

A: Given,  The equation, 16y2 -4x2 + z2 = 16

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…

Q: (3) Consider the quadric surface S C R, having equation a2 + y? - z2 = 9. Find all lines through P…

A: General equation of line from point 3,-3,3 is x,y,z=3,-3,3+tl,m,n.  Substitute it in the quadratic…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.