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## Homework Statement

There exist a curve C such that its parametric equation is (x,y,z)=(3−3t,1−t[tex]^{2}[/tex],t+2t[tex]^{3}[/tex]). There is a unique point P on the curve with the property that the tangent line at P passes through the point (−3,−2,2). Find the coordinates of P.

## Homework Equations

(C) : (x,y,z)=(3−3t,1−t[tex]^{2}[/tex],t+2t[tex]^{3}[/tex])

## The Attempt at a Solution

Attempt to solve it

(x',y'z')= (-3,-2t,1+6t[tex]^{2}[/tex] )

since the above is the direction vector of the tangent T then I tried to express the parametric equation of the tangent in function of t which has given me

x=-3s-3

y=-2ts-2

z=(1+6t[tex]^{2}[/tex])s+2

after that I tried to solve xp=x by replacing x in the line equation by the curve equation but I can't solve that !!! I really don't know how to approach this exercise ...

Thank you for your help