Answer to Question #194266 in Calculus for Bill

Question

Eliminate the parameter t.

x = 4 csc t - 4, y = 4cot t - 3

Answer 1

x = 4 $\cosec t$ - 4 ......................Equation(1)

y = 4 $\cot t$ - 3 .......................Equation(2)

We need to eliminate t, so from Equation (1) and (2) we have

$\cosec t$ = $\dfrac{x + 4}{4}$ ........................Equation(3)

$\cot t$ = $\dfrac{y+3}{4}$ .........................Equation(4)

We know that

$\cosec^2 t - \cot^2 t = 1$

From Equation (3) and (4) we have

$(\dfrac{x + 4}{4})^2$ - $(\dfrac{y+3}{4})^2$ = 1

Hence, the parameter t has been eliminated.