Question

Eliminate the parameter. 

x = t - 3, 

Answer 1

The parametric equation is x = t - 3 and y = 2/(t + 5)

Solve x = t - 3 for t.

Add 3 to each side.

⇒ t = x + 3.

Substitute x +3 for t in y = 2/(t + 5)

y = 2/((x + 3) + 5)

y = 2/(x + 8)

Cross multiplication.

(x + 8)y = 2

Subtract 2 from each side.

xy + 8y - 2 = 0.

This is the equation, after eliminating the parameter t.