Write the parametric equations x=3t−t^3, y=4−2t in the given Cartesian form. x= _________

Question

Write the parametric equations

x=3t−t^3, y=4−2t

in the given Cartesian form.

x= _________

Answer 1

y=4-2t,

solve for t

2t = 4-y,

t = 2-y/2

x=3t-t^3

substitute 2-y/2 for t

x = 3(2-y/2) - (2-y/2)^3

expand the cubed term using the formula (a-b)^3=a^3 -3a^2b + 3ab^2 -b^3 where a=2 and b=y/2

x= 6 - (3/2)y - (8 - 3(4)(y/2) +3(2)(y^2/4)- (y^3/8)

x = 6 -(3/2)y -8 + 6y - (3/2)y^2 + y^3/8

rewrite the polynomial in descending powers of y

x = (1/8)y^3 - (3/2)y^2 + (9/2)y - 8