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Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.
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• (1) x= sqrt t, y=4t+3; 0 ≤ t ≤ 4

A) y = - 3x ^ 2 + 19; 0 ≤ x ≤ 2
B ) y = - 3x + 19; 0 ≤ x ≤ 2
C) y=4x^ 2 +3; 0 ≤ x ≤ 2
D ) y=3x^ 2 +4; -1 ≤ x ≤ 2

• (2) x=2t, y=t+2; -2 ≤ t ≤ 3

A ) y=x ^2 + 1; - 2 ≤ x ≤ 2
B) y= 1/2x -2; -∞ C) y= 1/2x +2; -4 ≤ x ≤ 6
D ) y=-2x+2; -∞

Respuesta :

Answer:

1. C

2. C

Step-by-step explanation:

1. x = [tex]\sqrt{t}\\[/tex], y = 4t +3

Solve for t:

t = [tex]x^{2}[/tex]

Plug in t:

y = 4([tex]x^{2}[/tex] ) +3

y = 4[tex]x^{2}[/tex] +3

2. x = 2t, y = t + 2

Solve for t:

t = x/2

Plug in t:

y = 1/2x + 2

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