SOLUTION: Write as a single equation in x and y (a) {x=t+1, y=t^2-t} (b) {x= 3sqrt(t-1), y=t^2-t} (c) {x=sin(t), y=cos(t)}

Question 1157184: Write as a single equation in x and y
(a) {x=t+1, y=t^2-t}
(b) {x= 3sqrt(t-1), y=t^2-t}
(c) {x=sin(t), y=cos(t)}
Answer by Edwin McCravy(20063) (Show Source): You can put this solution on YOUR website!
Write as a single equation in x and y
(a)

 


Factor t out of the right side of the second equation"



Solve the first equation for t:


Substitute x-1 for t in the second equation:
    
leave it like that or FOIL out the right side:

(b) {x= 3root t-1, y=t^2-t}

Factor t out of the right side of the second equation"


Square both sides of the first equation:





Substitute (x²+9)/9 for t in the second equation:

This one's different. Use the trig identity sin²(θ)+cos²(θ)=1.



Leave it like that or solve for y.

Edwin

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