ALPHA DIVISION

Question 93

Parametric★★Question Bank

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Question

Of the following pairs of parametric equations, how many lie completely on the line

x+y=1

when graphed on the xy-plane?

I.\quad x(t)=\sin^2 t,\quad y(t)=\cos^2 t

II.\quad x(t)=-\tan^2 t,\quad y(t)=\sec^2 t

III.\quad x(t)=\csc^2 t,\quad y(t)=\sec^2 t

IV.\quad x(t)=\csc^2 t,\quad y(t)=-\cot^2 t

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Question

Of the following pairs of parametric equations, how many lie completely on the line

x+y=1

when graphed on the xy-plane?

I.\quad x(t)=\sin^2 t,\quad y(t)=\cos^2 t

II.\quad x(t)=-\tan^2 t,\quad y(t)=\sec^2 t

III.\quad x(t)=\csc^2 t,\quad y(t)=\sec^2 t

IV.\quad x(t)=\csc^2 t,\quad y(t)=-\cot^2 t