Consider the following 2nd order PDE, Uzz +2Uzy + 4U₂ = 0. (i) Write down its principal part and then determine the type (elliptic, parabolic or hyperbolic). (ii) Change the principal part of the above equation to a canonical form (i.e. without cross-derivatives).

Q: 2. For the equation 2x² + 2xy + 2y²-2x-10y+11= 0, eliminate the xy term by rotating the coordinate…

A: Given: The given equation of the conic is 2x2+2xy+2y2-2x-10y+11=0.                      ...........1…

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Q: 1.) Find the derivatives of a.) y = 3e²x — 2lnx + arcsec x

A: the given equation is

Q: 3) Find an equation of the tangent line to the graph of y = (z + 4)² at z = 4.

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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Q: x=t3/3  y=t2/2     0<t<1  resolve the parametric equation

A: Given that , x=t3/3  y=t2/2     0&lt;t&lt;1  Resolve the given parametric equation.