Obtain the differentialequation of the family of ellipses w/center at (0, 0) having major and minor axes respectively alongx and y axis and minor axis is equal to one-third of the major axis. Show your complete solution. Final answer must be in Differential form.

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Q: Find the differential equation of the family of ellipses with center at the origin a and the major…

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A: Parametric equation of the ellipse x2a2+y2b2=1 is given by x(t)=a cosθ, y(t)=b sinθ, t∈[0, 2π]

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Q: Find an equation for the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

A: Our Aim is to find an equation for the surface of revolution formed by revolving the curve 2x+3z=1…

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Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2…

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Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

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Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

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Q: of the solid in revolution as it axis and the function 2 – x) 0<x< 2

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Q: Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point…

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