Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius VC.

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Find a vector-valued function whose graph is the indicated surface.

A: To find :               Find the vector valued function whose graph is the indicated surface.

Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

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Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

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Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: Find an equation of the tangent plane to the surface xyz = 10, at the given point (1, 2, 5), and…

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Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

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Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Find a parametrization for the line segment beginning at P1 and ending at P2. 25) P1(-4, –5, 4) and…

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Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 =…

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Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

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Q: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given point (2, 2, 8)…

A: To Determine: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given…

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

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Q: find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. y =…

A: Consider the provided curve, y=cx2 Find the orthogonal trajectories of the family ofcurves. First…

Q: Find an equation of the tangent plane to the surface z=−1x2+3y2−3x+1y+1 at the point (2, 2, 5).

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Q: Find the equation for the tangent plane to the surface -3x+ 9y -7z = -26 at the point (1,-1, Lütfen…

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Q: Find the least squares quadratic & bj xj which best fits curve Y = sin(x)

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Q: Find the distance from the point (3, 4, -1) to the plane lr 3y +2z = 5.

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Q: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…

A: As the given plane tangent to z=f(x,y) at (-2,3,4) is  4x+2y+z=2, that is z=2-4x-2y thus the…

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied…

A: Here, a semi-circle is of radius 3.

Q: Obtain the dirfferential equation of the family of curves:  1. All circles passing through the…

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Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2 at the point (2,1,-30)

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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 the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: Find an equation of the tangent plane to the surface at the given point. fx, у) %3 х2 - 2ху + у2,…

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Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

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Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: Find the equation of the tangent plane to the surface 2x^2 -xz + y^2 -zy = -5 at the point (1, 3, 4)

A: First we find out partial derivative at given point and then find the equation of the tangent plane…

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 the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: Determine the orthogonal trajectories of the family of circles (equation below) that is tangent to…

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle 0…

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Q: Find the tangent plane and normal line equations to x+y +z =1 at the point (1, %3D -2, -4).

A: This question is related to 3D geometry and equations of plane and lines,  we will solve it using…

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Use a linear approximation to estimate V29. Show the work. Do not round your

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Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

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Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…