Given the parametric equatiins x = 4/(t+3)^2 and y=12/t+3, find the value of parameter t if dy/dx = 9

Question

Given the parametric equations x = 4/(t+3)^2 and y = 12/t+3, find the value of parameter t if dy/dx =9

 

Answer 1

You want to get "t" in terms of "x".

 

x(t + 3)² = 4

 

(t + 3)² = 4x^-1

 

t + 3 = (4x^-1)^1/2

 

t = -3 + 2x^-1/2

 

 

Plug this into y, then find the derivative of y.  Then, set the derivative equal to 9 and solve for x.  When you have x, plug it back into the bolded equation to find t.