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Eliminate the parameter t to determine a Cartesian equation for: x = t^2, y = 8 + 4t.

Question:

Eliminate the parameter {eq}t {/eq} to determine a Cartesian equation for: {eq}x = t^2, \; y = 8 + 4t {/eq}.

Cartesian Equation of a Curve:

In this problem, we need to write the Cartesian equation of the given curves {eq}x=f(t) , y = g(t) {/eq}

So we need to equate the parameter {eq}t {/eq} in terms of {eq}x , y {/eq} and simplify to get the desired solution.

Answer and Explanation:

We are givn:

{eq}x = t^2 \Rightarrow t =\sqrt{x} \\ {/eq}

Next, {eq}y = 8+4t \Rightarrow 4t = y-8 \Rightarrow t = \dfrac{y-8}{4} \\ {/eq}

Now...

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from PSAT Prep: Tutoring Solution

Chapter 10 / Lesson 13
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