Parametric given the rectangular equation and one parametric equation

Question

y=2sqrt(2x-3)+5; Domain x = (4,8); x(t) = 3t-5

Answer 1

 

y = 2*sqrt(2(3t-5)-3) + 5

 

   = 2*Sqrt( 6t - 13) + 5

 

 

 

x = 3t-5 ----> (x+5)/3 = t

 

      The given domain is ( (4+5)/3 ,  (8+5)/3 ) = (3,13/3) = (3, 26/6)

 

 

 But 6t-13>=0 ---> 6t >=13 ----> t >=13/6

 

So the real domain is (13/6,26/6) = (13/6, 13/3)