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Find a direct relationship between y and x.
x = √3t and y = 12t + 9

for x ≥ 0

User Yasirnazir
by
7.9k points

1 Answer

7 votes

Answer:


y=4x^2+9

Explanation:

Given parametric equations:


x=√(3t),\qquad x \geq 0


y=12t+9

To find a direct relationship between y and x, begin by rearranging the first equation to isolate t:


\begin{aligned} x&=√(3t)\\\\x^2&=(√(3t))^2\\\\x^2&=3t\\\\(x^2)/(3)&=(3t)/(3)\\\\t&=(x^2)/(3)\end{aligned}

Substitute the found expression for t into the equation for y:


\begin{aligned}t=(x^2)/(3) \implies y&=12\left((x^2)/(3)\right)+9\\\\y&=4x^2+9\end{aligned}

Therefore, the direct relationship between y and x is:


\boxed{y&=4x^2+9 \quad \textsf{for}\;x \geq 0}

User Anthony Hervy
by
8.1k points