Find equations of the following x2 — Зу? + z? + yz %3D 6, (7, 4, -5) (a) the tangent plane 14х — 29у — 62 —D 12 (b) parametric equations of the normal line to the given surface at the specified point. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

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 line through (7,4, – 7) perpendicular to the plane 4x + 5y + 4z =…

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: 12- Find an equation of the tangent plane to the given parametric surface at the specified point.…

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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 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 for the line through (- 1,6, - 1) perpendicular to the plane 7x+ 5y + 5z =…

A: to find the parametric equations for line passing through (-1, 6, -1) and perpendicular to the…

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y? z1…

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given surfaces are And the given point P is

Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

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Q: Find a parametric equation for the line through the point(1,9,3) and perpendicular to the plwne…

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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: Find parametric equations for the normal line to the surface z= 3x2 + 10y2 at the point (2, 1, 22).…

A: Given the equation of surface z=3x2+10y2

Q: Consider the surface r²+y²+2ry-3x+2y-2z=1. Determine the following: (a) the general equation of the…

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Q: I am working with cal 3. How do I find the parametric equations of the line for the intersection of…

A: The parametric equations of a line through the point (x0, y0, z0) and parallel to the direction…

Q: z = In(x²y*) + / x² + y²

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Q: Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 6) i+ (v³…

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Q: Find parametric equations of the normal line to the surface z = + y? at the point (2, -2,5) x = 2 -…

A: Let F(x,y,z) define a surface that is differentiable at (x0,y0,z0) then the normal line to F(x,y,z)…

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

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Q: Find parametric equations of the normal line to the surface z = 4 + y² at the point (2, –2, 5) |

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Q: Find equation of the tangent plane to the given surface at the specified point. 5x^2+3y^2+8z^2,…

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Q: Find parametric equations for the normal line to the surface x2 + 9xyz + y² = 11z2 at the point (1,…

A: Given:- x2+9xyz+y2 =11z2  To find:- Equation of normal line to the given surface at point (1,1,1)

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

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 the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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

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

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Q: A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At…

A: Given Motion is a circular motion. r = radius of the circlea = x-cordinate of the centreb =…

Q: ) Consider an object moving in the plane according to the parametric equations x = 26te z – 676e , y…

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

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Q: Find the parametric equation of the line tangent to the curve of intersection of the cylinder…

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

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Q: Use definition 13.7.1 to find the equation of the tangent plane and the parametric equations for the…

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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 the equations of the tangent plane and normal line to the surface with equation 9y? + 9z2 = 22…

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Q: 1. Calculate the distance from the point P(9,4, 3) to the line which contains points A(1, 0, 1) and…

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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 line tangent to the curve of intersection of the surfaces tan-1(x?…

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Q: Eliminate the parameter in x = -t +2t and y =t-4 and then identify the parametric curve and sketch…

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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 +…

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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: 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 an equation of the tangent plane to the surface z = √(9 − x2 − y2), at the given point (1, 2,…

A: The surface given is Fx,y,z=√(9 -x2 -y2) -z =0. The derivative of the surface coordinates with…

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: Find equations of the following. x² - 3y2 + z2 + yz = 6, (7, 4, -5) (a) the tangent plane (b)…

A: a) tangent plane: