Question

Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for:

x(t) = -4 t^2
y(t) = -4 + 2t
 

 

Answer 1

The parametic equation is x(t) = - 4t²  y(t) = - 4 + 2t

x = - 4t² , y = - 4 + 2t

y = -4 + 2t

Solve for t.

y + 4 = 2t

t = (y + 4)/2

Substitute t = (y + 4)/2 in x = - 4t²

x = - 4[(y+4)/2]²

x = -4 [ (y +4)² / 4]

x = - y²  - 16 - 8y