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Eliminate the parameter “t” for the parametric equations, where 0 < t < 5.


x = √5t

y = 2t — 2


Answers:

A) y = 2/5x^2 — 2
B) y = 5/2X^2 — 5
C) y = 2√5x — 2
D) y = 2/5x^2 — 2

Respuesta :

elcharly64

Answer:

A) y = 2/5x^2 — 2

Step-by-step explanation:

We are given the parametric equation:

[tex]x=\sqrt{5t}[/tex]

[tex]y=2t-2[/tex]

To express y in terms of x, we solve for t in the first equation and substitute in the second equation.

Squaring:

[tex]x^2=(\sqrt{5t})^2[/tex]

[tex]x^2=5t[/tex]

Solving for t:

[tex]\displaystyle t=\frac{x^2}{5}[/tex]

Substituting in the second parametric equation:

[tex]\displaystyle y=2\frac{x^2}{5}-2[/tex]

[tex]\displaystyle y=\frac{2}{5}x^2-2[/tex]

Correct choice: A) y = 2/5x^2 — 2