Question #194266

Eliminate the parameter t.


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


1
Expert's answer
2021-05-27T09:37:27-0400

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

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



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


cosect\cosec t = x+44\dfrac{x + 4}{4} ........................Equation(3)


cott\cot t = y+34\dfrac{y+3}{4} .........................Equation(4)


We know that


cosec2tcot2t=1\cosec^2 t - \cot^2 t = 1


From Equation (3) and (4) we have


(x+44)2(\dfrac{x + 4}{4})^2 - (y+34)2(\dfrac{y+3}{4})^2 = 1


Hence, the parameter t has been eliminated.




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