O Given Fley,e)= <6x,- 4z,-4y> Use the parametric descriphion CiP(H = , oŚ€€ to directly evalvate the line integral SE«Tds. ® Find a patential function $s, y, 2)., such that ♡$ = F. © Use the potential fuection found in part B aud thke Fundamental Theo tem of Line Integ rals to evaluate the lme integral ŞETds in part A.

Q: Find the coordinnates of a point on the oarabola y\power{2}=8x whose focal distance is 4.

A: Parabola.  y2=8x.  and Focal distance = 4

Q: Find the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

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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: A particle travels in the xy -plane with a path defined by the parametric equations x(t) = t - 3 and…

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Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: Investigate the direction of convexity of the curve defined by the parametric…

A: To Determine: The direction of convexity of parametric curves x(t)=a(t-sint) , y(t)=a(1-cost) ,…

Q: How can I parametrize this 3D shape with two variables? x ≥ 0, 0 ≤ y ≤ x, x^2 + y^2 ≤ z ≤…

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Q: Ř(u, v) = (u², v – 2u, u + v²)

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Q: Q2/ Find the Parametric aned standand equatior of the line Hhat passer through Points (-2,1,0)…

A: The equation of line passing through given two points is given as follows:

Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

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Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x =…

A: Let's find the total distance covered. = d

Q: Write an equation in general form of the tangent plane to the surface x^2+siny + z^3 = −4 at the…

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Q: Give a parametric representation for the straight line segment from the point (1,-1,2) to the point…

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Q: Parametrize y = -x2 + 4 in terms of u and v %3D

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Q: Show that the line of slope t through (-1, 0) intersects the unit circle in the point with…

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Q: convert parametrici equation in rectangualr form  x=5sin t, y=4cos t

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Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k

Q: Distinguish briefly the Parametric and non-parametric analysis

A: There are two types of analysis in the testing of the hypothesis. they are: 1) Parametric analysis.…

Q: Parametrize the circle of radius 7 centered at (-2, 3) in the clockwise direction starting at…

A: Here I am attaching image so that you understand each and every step.

Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

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