Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane −12x + 2y + 6z = 0.

Q: Find the equation of the tangent plane to the surface y = 2x2 - z at the point %3D (0, -1,-2) y+2z =…

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Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Find the equation of the tangent plane to the surface 4xe^yz+xz^2−7x^3y= 5 at(1,0,1).

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Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

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Q: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

A: Given  and plane

Q: Find a point on the ellipsoid x + 3y² + z = 8 where the tangent plane is perpendicular to the line…

A: Introduction: The perpendicular vector to a 3D object f ( x, y, z ) can be calculated by computing…

Q: Find the slope of the tangent line at the point (1,−2,−3) on the curve of intersection of the…

A: Given surface is z=5-4x2-y2 The slope of tangent line to the curve that is the intersection of the…

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

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Q: Find a vector tangent to the curve of intersection of the surfaces given by x² + y² + z² = 1 and 2²…

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Q: Find the angle of inclination of the tangent plane to the ellipsoid                           x2/ 12…

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Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

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

A: The given curve is the intersection of paraboloid z = x2+y2 and ellipsoid 3x2+2y2+6z2 = 29.

Q: Find an equation of the tangent plane to the surface z=8/2x+4y at the point (2,1,1). z=

A: Please see the explanation below

Q: 5) Find the equation of the tangent plane to the surface exyz= x + 2y + 3z at the point (3,-1,0).

A: Find tangent plane to the surface

Q: Find the points on the surface 2a2 + ly² + 522 = 1 at which the tangent plane is parallel to the…

A: We will use the following method for finding the two required point.

Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

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Q: A point moves along the intersection of the elliptic paraboloid z = x + 3y² and the plane y = 3. At…

A: z=x2+3y2 and y=3 Point of Intersection : Curve z:x2+3y2=x2+3(3)2=x2+27 dzdx=2x+0 =2x

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

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

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Q: Compute the equation of the plane tangent to the surface x^2+3 y^2+z^3 = 8 at the point (2,1,1).

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Q: Find the equation on the plane tangent to the following surfaces at a given point: z=exy; (2,0,1)…

A: The equation on the plane tangent to the surface z = f(x, y) at a given point (a, b, c) is given by:…

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: The equation of the tangent plane at the point P(1, 1,-1) on the surface z = f(x, y) = 4 - -* is x +…

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Find the equation for the tangent plane to the surface z= 7x2. 10y² at the point (2, 1, 18). O 2x +…

A: Equation for the tangent plane to the surface z=f(x, y) at the point (a, b, f(a, b)) is given by

Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

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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: Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the…

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Q: Find equation of line normal to plane 3x + 2y – z = 5 and pass througl Origin point.

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Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Find the equation of tangent plane to the surface x² + 2y? + 3z2 = 21 which is parallel to the plane…

A: Topic- equation of tangent to surface

Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

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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…

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Q: Find an equation of the tangent plane and symmetric equations of the normal line to the surface zx2…

A: Given the equation of the surface can be rearranged in the form F(x,y,z)=0 zx2-xy2-yz2-18=0 Here,…

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: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

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

A: To find: The parametric equations for the tangent line to the curve of the intersection of the…

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

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Q: Find the equation of tangent plane to the surface z = ln (3x²) + 2y at A (1,0, In (3)).

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Q: Find the equation of the tangent plane to the surface y = 2x - z at the point (0, -1,-2) y+2z = -5…

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Q: b) Find the equations of Tangent plane and Normal line of the surface: z3 + xyz – 2=0 at Po(1,1,1)

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Q: Find the equation of the tangent plane to the surface y = 2x2 (0, –1, 2) z at the point O y+ 4z = 7…

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Q: Find the moment of inertia of the solid formec y2 = 2x and th

A: Introduction: If a solid is formed by revolving an area about the y-axis, then the moment of inertia…