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I can't figure out how to do this problem. Any help would be appreciated.

Given that the curve C is defined by x=t^2-4, y=t^3+1,z=5te^(t^3+1), write an equation (in rectangular form and with integral coefficients and constants) for the normal plane to C at P (-3,0,-5).

Edit: Here's what I've done. I have no idea how much is right though. The point exists where t=-1.

x'=2t, y'=3t^2, z'=5e^(t^3+1)+15t^3e^(t^3+1)

x=2*-1=-2, y=3*(-1)^2=3, z=-10

-2x+3y-10z= -2*-3 + 3*0 + -10*-5

-2x+3y-10z=56

Anyone know if this is correct?

Given that the curve C is defined by x=t^2-4, y=t^3+1,z=5te^(t^3+1), write an equation (in rectangular form and with integral coefficients and constants) for the normal plane to C at P (-3,0,-5).

Edit: Here's what I've done. I have no idea how much is right though. The point exists where t=-1.

x'=2t, y'=3t^2, z'=5e^(t^3+1)+15t^3e^(t^3+1)

x=2*-1=-2, y=3*(-1)^2=3, z=-10

-2x+3y-10z= -2*-3 + 3*0 + -10*-5

-2x+3y-10z=56

Anyone know if this is correct?

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