Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y² and the ellipsoid 3x2 +2y² + z² = 9 at point (1,1,2) as shown in figure below. (1, 1, 2)

Q: What is the parametric equation of line through the point (1,2, -1) and perpendicular to the plane…

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Q: parametric

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

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Q: Find the parametric equation for a line that is tangent (intersection) of the two fields below: −2x…

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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 the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

A: We know that the parametric equation of a tangent line to the curve of intersection of the two…

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

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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: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

Q: find a parametrization for the curve. the ray (half line) with initial point (-1, 2) that passes…

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Q: 27. Show that the curve with parametric equations x = t cos t, y =t sin t, z = t lies on the cone z²…

A: To Show: i. Show that the curve with the parametric equationx=tcost, y=tsint, z=t  lies on the…

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

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Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

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

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Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

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

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

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

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Q: Graph the curve with parametric equations x = sin(t), y = 3 sin(2t), z = sin(3t). H0.0 y -0.5 0.5…

A: The graph will look like this:

Q: find a parametrization for the curve. the ray (half line) with initial point (2, 3) that passes…

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Q: 5. Find the distance from the point (3, 0, 10) to the plane 2x+3y+ z = 2. 6. Write the parametric…

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Q: Find parametric equations of the line through the point (5, 0,−2) that is parallel to the planes x…

A: Any point in three dimensional coordinate system will be of the form x1,y1,z1 . We can calculate the…

Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

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Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

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Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 7y and the planex = 1. At…

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

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

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Q: Find an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

A: Solved below...

Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

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: 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: 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 the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

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Q: Let C be the curve of intersection of the spheres x 2 + y 2 + z2 = 3 and(x - 2)2 + (y - 2)2 + z2 =…

A: Let fx=x2+y2+z2-3=0 & gx=x-22+y-22+z2-3=0 At P=(1, 1, 1) ∇f=2x, 2y, 2z∇fP1, 1, 1=2, 2, 2…

Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

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

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Q: Find an equation for the tangent plane to the hyperboloid x2+y2−z2=1 at the point (3,1,3).

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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 equation of the plane tangent to and the line (in symmetric form) normal to the ellipsoid…

A: Given:   x2+ 4y2 +8z2 = 48 Point : ( -2 , 3 , -1)

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

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Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

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Q: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…

Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

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