By means of Stokes' Theorem, find | F. dŘ 3.x, on the ellipse x² + y? = 1, z = F = xỉ+ (x + y)3+ (x + y + z). The ellipse is traced counterclockwise if we look back at it from the direction of the positive z-axis.

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).

A:

Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

A:

Q: Sketch the following surfaces. 1) 4x^2+9z^2=9y^2 2)y^2-x^2=z Show all work.

A:

Q: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A:

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: Use the parametric equations of an ellipse, x = 5 cos(0), y = 3 sin(0), 0 ≤0≤2π, to find the area…

A:

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: Find the area of the ellipse x^2+14 x y+245 y^2=4 by using a suitable transformation that maps to…

A: Given equation is, x2+14xy+245y2=4 The equation can be written as,…

Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = = sin 0, 0 E…

A:

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

A:

Q: Find the transformation that makes the ellipse: (x^2 / a^2) + (y^2 / b^2) = 1, into a unit circle…

A: Find the transformation that makes the ellipse: (x^2 / a^2) + (y^2 / b^2) = 1, into a unit circle.

Q: tangent plane at the point (-2,1 – 3)

A: Equation of the tangent plane = dfdxx-x0+dfdyy-y0+dfdzz-z0 Let f=x24+y2+z29-3 (given)

Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

A:

Q: Consider the equation 4y^2 + z^2 − 4x − 8y + 4z + 8 = 0. Then classify the surface it represents…

A: Given equation of surfaces 4y2+z2-4x-8y+4z+8=0

Q: Find the equation of the surface of revolution generated by rotating the parabola y = z^2 around the…

A: A surface of revolution generated by rotating a curve described by y=f(z) around z-axis is given as…

Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: Find the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A: The plane z=11-3x+2y and cylinder is x2+y2=9. Obtain the partial derivatives of z=11-3x+2y:…

Q: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

A:

Q: The locus of the foot of the perpendicular from the centre of the hyperbola xy = c² on a variable…

A: Given hyperbola equation is  xy = c2 The parametric form of this hyperbola is  x = c t  and   y =…

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

A:

Q: The surface of a paraboloid results from rotating a parabola about its axis. the parametric form is…

A: The objective of the question is to understand how the shape of a paraboloid changes when the…