
The graph of the curve of a parametric equation x=t+2, y=√t ; t≥0, show its orientation. Find the rectangular equation of curve.

Answer to Problem 9AYU
Solution:
The graph of the parametric equations x=t+2, y=√t ; t≥0 is
The rectangular equation of the parametric equation x=t+2, y=√t ; t≥0 is x−y2=2.
Explanation of Solution
Given information:
The parametric equation x=t+2, y=√t ; t≥0
Explanation:
To draw the given parametric equation, plug some values of t in the given equation and find few points on the curve.
The interval for t is t≥0
tx=t+2y=√t(x, y)020(2,0)131(3,1)24√2(4,√2)35√3(5,√3)46√4(6,2)
The orientation is curve traced out in a certain direction by the corresponding succession of points (x,y).
The arrow shows the orientation along the curve as t varies from t≥0.
As t takes values from t≥0, the corresponding orientation is from (2,0) to (6,2)
Use points in the table to sketch the curve.
The graph of the parametric equation x=t+2, y=√t ; t≥0 is
Let x=t+2 ——- (1)
y=√t ——– (2)
Solve equation (1) for the variable t ,
⇒x−2=t
Substitute this result for t into equation (2),
⇒x−2=y2
⇒x−y2=2
The rectangular equation of the parametric equation x=t+2, y=√t ; t≥0 is x−y2=2.
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