Question
Rewrite the parametric equations
x=92(y−2)2
Evaluate
y=3t+2x=2t2
Choose the parametric equation
y=3t+2
Solve the equation
t=3y−2
Solution
x=92(y−2)2
Show Solution
![solution-arrow](data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMTciIGhlaWdodD0iMTYiIHZpZXdCb3g9IjAgMCAxNyAxNiIgZmlsbD0ibm9uZSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KPHBhdGggZD0iTTguNSAyLjY2Nzk3TDguNSAxMi42NjgiIHN0cm9rZT0id2hpdGUiIHN0cm9rZS13aWR0aD0iMS41IiBzdHJva2UtbGluZWNhcD0icm91bmQiIHN0cm9rZS1saW5lam9pbj0icm91bmQiLz4KPHBhdGggZD0iTTEyLjUgOC42Njc5N0w4LjUgMTIuNjY4TDQuNSA4LjY2Nzk3IiBzdHJva2U9IndoaXRlIiBzdHJva2Utd2lkdGg9IjEuNSIgc3Ryb2tlLWxpbmVjYXA9InJvdW5kIiBzdHJva2UtbGluZWpvaW49InJvdW5kIi8+Cjwvc3ZnPgo=)
Find the first derivative
dxdy=4t3
Evaluate
y=3t+2x=2t2
To find the derivative dxdy,first find dtdx and dtdy
dtd(y)=dtd(3t+2)dtd(x)=dtd(2t2)
Find the derivative
More Steps
![solution-arrow](../../wwwstatic/images/solution-arrow-down-1.svg)
Evaluate
dtd(y)=dtd(3t+2)
Calculate the derivative
More Steps
![solution-arrow](../../wwwstatic/images/solution-arrow-down-2.svg)
Evaluate
dtd(y)
Use differentiation rules
dyd(y)×dtdy
Use dxdxn=nxn−1 to find derivative
dtdy
dtdy=dtd(3t+2)
Calculate the derivative
More Steps
![solution-arrow](../../wwwstatic/images/solution-arrow-down-2.svg)
Evaluate
dtd(3t+2)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
dtd(3t)+dtd(2)
Calculate
3+dtd(2)
Use dxd(c)=0 to find derivative
3+0
Removing 0 doesn't change the value,so remove it from the expression
3
dtdy=3
dtdy=3dtd(x)=dtd(2t2)
Find the derivative
More Steps
![solution-arrow](../../wwwstatic/images/solution-arrow-down-1.svg)
Evaluate
dtd(x)=dtd(2t2)
Calculate the derivative
More Steps
![solution-arrow](../../wwwstatic/images/solution-arrow-down-2.svg)
Evaluate
dtd(x)
Use differentiation rules
dxd(x)×dtdx
Use dxdxn=nxn−1 to find derivative
dtdx
dtdx=dtd(2t2)
Calculate the derivative
More Steps
![solution-arrow](../../wwwstatic/images/solution-arrow-down-2.svg)
Evaluate
dtd(2t2)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dtd(t2)
Use dxdxn=nxn−1 to find derivative
2×2t
Multiply the terms
4t
dtdx=4t
dtdy=3dtdx=4t
Solution
dxdy=4t3
Show Solution
![solution-arrow](data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMTciIGhlaWdodD0iMTYiIHZpZXdCb3g9IjAgMCAxNyAxNiIgZmlsbD0ibm9uZSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KPHBhdGggZD0iTTguNSAyLjY2Nzk3TDguNSAxMi42NjgiIHN0cm9rZT0id2hpdGUiIHN0cm9rZS13aWR0aD0iMS41IiBzdHJva2UtbGluZWNhcD0icm91bmQiIHN0cm9rZS1saW5lam9pbj0icm91bmQiLz4KPHBhdGggZD0iTTEyLjUgOC42Njc5N0w4LjUgMTIuNjY4TDQuNSA4LjY2Nzk3IiBzdHJva2U9IndoaXRlIiBzdHJva2Utd2lkdGg9IjEuNSIgc3Ryb2tlLWxpbmVjYXA9InJvdW5kIiBzdHJva2UtbGluZWpvaW49InJvdW5kIi8+Cjwvc3ZnPgo=)