EXAMPLE 9 Find the tangent plane to the surface with parametric equations x = u2, y = v2, z = u + 2v at the point (1, 1, 3).

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

A:

Q: Question 4 Evaluate fVdr which V given by V = xy + 2xy + yz between A(0,0,0) and B(2,1,3) along the…

A:

Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

Q: 25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone…

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z =x²…

A: Tangent line to ellipse will be perpendicular to normals of both the surfaces Therefore,  The…

Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

A:

Q: Find the parametric equations for the curve of intersection between the cylindrical surface S: x +…

A:

Q: Find normal line (parametric form) to the surface x^2 − 4y^2 + z^2 + y = 27 at the point (5, 1, −3

A: This question is about application of derivative

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

A:

Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y³ + z²…

A:

Q: Find a point on the ellipsoid x² + 2y2 + z2 = 19 where the tangent plane is perpendicular to the…

A:

Q: Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the…

A: First, find the function of the surface in three variables, f(x,y,z).  f(x,y,z)=x2y-z Find the…

Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

Q: 15. Find the radius of curvature at 0 = -n of the parametric equations x = 3(0 + cos 0), y = 3(1 –…

A: For the parametric curve x=x(θ), y=y(θ)Curvature K=|x'y''-y'x''|[(x')2+(y')2]32Radius of…

Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: 2. Find parametric equations for the line tangent to the curve of intersection of the surfaces at…

A:

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

A:

Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

A:

Q: Find a parametric equation for the curve of intersection of the cone x²+y² = z² and the plane x+2z =…

A: We have to find a parametric equation for the curve of intersection of the cone x2+y2=z2 and the…

Q: Find a parametric equation for the line tangent to the curve of the intersection of the surfaces at…

A:

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² + ¹/² = 4…

A: We need to obtain a set of parametric equations for the curve of intersections of the cylinders:…

Q: Find the 1st  and 2nd Derivate of y with respect to x from parametric equations. Complete solution…

A:

Q: A particle moves in space along a path whose parametric equations are given by bsin(wt), x2 =…

A: Image is attached with detailed solution.

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given To find parametric equations for the tangent line to the curve with the given parametric…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given parametric equation is: x=5 ln t  ,   y=4t   ,      z=t3 Given point is:  (0, 4, 1) From…

Q: Given the surface z = In(5x2 + 2xy - 3y2 – 12). (a) Find the equation of the tangent plane and the…

A:

Q: Find an equation of the tangent plane and a parametric description of the normal line to the surface…

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x²…

A: Given :-  The curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid x2 + y2 + z2 =6…

Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

A: We know that equation of plane which passes through pointx1,y1,z1 and perpendicular to linex=x2+at,…

Q: Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line…

A: Given  The equation of ellipsoid is given by fx,y,z=x2+4y2+z2-9 The line is x=2-4t, y=1+8t and…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point.  x = u…

A:

Q: The equation of the tangent plane to the surface defined by z y exp(-x) at the point (0, 1, 1) is =…

A: equation of the tangent plane

Q: Consider the equation of the surface S given by: exyz + x3z3 − 3y4 = 9 An equation for the plane…

A:

Q: The two surfaces x2 + y2 + z2 = 6 and 2x² + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: Given: The two surfaces  x 2 + y 2 + z 2 = 6  and  2 x 2 + 3 y 2 +  z 2 = 9. The given two surfaces…

Q: The tangent plane equation of the level surface z =-x² – 3y² at point (2,2,-16) is. O a.…

A: Given: The tangent plane equation of the level surface z=-x2-3y2 at point (2,2,16)

Q: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

A: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). %3D

A: Given that XY3 Z2 =2 And point (2, 1,-1).

Q: Find a rectangular equation for the plane curve defined by the parametric equations. x = 6 sin t, y…

A:

Q: Find the equation of the tangent plane to the surface 3D1 16 at the point (1,-3,2) O a. 2x+4y-3z=12…

A:

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2…

A: Tangent line to ellipse will be perpendicular to normal's of both the surfaces.  Therefore tangent…

Q: Find the parametric equations for the curve of intersection between the cylindrical surface S : x +…

A:

Q: At what point on the ellipsoid 2x^2 + y^2 + z^2 = 1 is the tangent plane parallel to the plane x + y…

A:

Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

A: Given surfaces, x2+2y+2z=4     and   y=1f(x,y,z)=x2+2y+2z-4          and   f(x,y,z)=y-1  And point…

Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

A:

Q: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

A:

Q: If I have a pair of parametric equations  x=20cos(t) and y=10sin(t)  How can I increase the speed…

A: