Which one of the following is a set of symmetric equations for the line normal to the surface given by xy+z=1 at the point (1,-2,3)? Select one: xy+z-1=0 x=1-2t, y= -2+t, z=3+t, -∞

Q: nd symmetric equations of the tangent line to the curve of intersection of the surfaces z = x² + y²,…

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

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: Which one of the following is a set of symmetric equations for the line normal to the surface given…

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Q: Which of the following is the equation of the plane that is tangent to the surface 2 x² + y? – x z –…

A: Consider the provided information, The provided surface, 2x2+y2-xz-3z=1 Find the partial derivative…

Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

Q: Find parametric equations of the normal line to the surface z = 4 +y? at the point (2, 3, 10) O x =…

A: To Find:  the parametric equations of the normal line to the surface  z = x24+y2 at the point ( 2,…

Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

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Q: The equation of the tangent plane to the surface at the point (-2, 1, 3) is Select one: = -(x-2) +…

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Q: Let (P) be the surface of equation 2x+4y² =16 and (Q) be the surface of equation x=-1-3y²-3-². Then…

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Q: Find the point(s) on the surface z2 = xy+1 which are closest to the point (10, 8, 0). List points as…

A: The objective is to find the points on the surface z2=xy+1 which are the closest to the point 10,8,0…

Q: A 2-D surface was found in one research group of scientists and a surface equation has been derived…

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Q: An equation of the tangent plane to the surface y = 3 x-z at the point (-2,8, 2) is: (A) 12 (x+2) +…

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Q: Find the equation of the tangent plane to the surface =1 16 at the point (1,-3,2) O a. 3x-2y+z=24 O…

A: Given: x24+y29+z216=1 x,y,z=1,-3,2. Simplify the equation.…

Q: Which of the given points are the points on the hyperboloid x2-y?+4z2 = 4 where the normal line is…

A: Solution is in step 2

Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: 8) Find equations of (a) the tan gent plane and (b) the normal line to the given surface at the…

A: Tangent plane: It is defined as the plane which passes through the surface of the points or it can…

Q: Which of the following correctly represents the plane region in the first quadrant bounded by the…

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Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: The equation of the tangent plane to the surface x² z² at the point (-2, 1, 3) is Select one: + 2y.…

A: To find the equation of tangent plane.

Q: An equation of the tangent plane to the surface y = 3 x-z at the point (-2,8, 2) is: %3D (A) 12…

A: y = 3x2 -z2 at the point (-2,8,2)f(x,y,z) = 3x2 - z2 -y∂f∂x = 6x, ∂f∂y = -1, ∂f∂z = -2zat point…

Q: 2. Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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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: 4. Let f(x, y) = V2x² – 3y². (a) What is the domain of this surface? (b) Draw three level curves of…

A: This is a problem of analysis of several variables. Contour and trace a graph.

Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: An equation of the straight line normal to surface x2 - y3 + z = 8 at the point P(2, -1, 3) on the…

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Q: Given a surface f(x,y) = -3x2 + (4)y2. Find the derivative in the direction of v = at the point (1,…

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Q: An equation of the tangent plane to the surface x = 3 y2 - z2 at the point (8, –-2,2) is: %3D (A) (x…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 5, 4) (b)…

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Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

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Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: Let (S) be the surface given by the following equation. In(2x + y) = ze* +3y. %3D An equation of the…

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Q: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 +…

A: It is required to find the equation of generating curve given the equation of its surface of…

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

A: parameterisation

Q: Find the equation of the tangent plane to the surface 4 =1 at the point 16 9 (1,-3,2) O a.…

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Q: 2. Let a, b, and c be three nonzero constants. Show that the equation of the tangent plane to the…

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Q: 22 2 Find the equation of the tangent plane to the level surface xy*z? (– 1, – 1, – 2) = 4 at the…

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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: Find the equation of the plane that passes through the point (2, 1, 7) and is tangent to the surface…

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Q: Find parametric equations for the normal line to the surface -10x + 5y + 9z =3 at the point (1, -…

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Q: The equation of the normal line to the surface X - y² – z² = 1 through the point (3, –1, 1) is O a)…

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Q: Find an equation of the tangent plane to the surface x-xyz 56 at the point (-4,5,2). Select one:…

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Q: Find the point of intersection between the surface y=9 and the tangent line to the curve of…

A: Find the intersection curve for the given two surfaces by solving the equations by the method of…

Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz=1…

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

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

Q: The equation of the tangent plane to the surface a2- 3y2 – 22 +3 = 0 at the point (2, -1, -2) is…

A: We will find the equation of tangent plane m

Q: An equation of the tangent plane to the surface z = 2 y-x at the point (2,-2, 4) is: (A) 4 (x – 2) +…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Which of the following is true about the pathway of the graph for the parametric equations belov…

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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…