For the Parametric Curve: X = 6t, Y = 108t²

question 29

Essay

For the parametric curve: x = 6t, y = 108t², eliminate the parameter and express in rectangular form.

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Definitions:

Square Root Property

States that if x^2 = a, where a is a non-negative real number, then x = ±√a, identifying two possible solutions for x.

Factoring

The process of breaking down an expression into its simpler components or factors that, when multiplied together, result in the original expression.

Square Root Property

A principle stating that for any positive number \(x\), if \(y^2 = x\), then \(y\) is a square root of \(x\).

Complex Solutions

Solutions to equations that include the square root of a negative number, typically represented as a combination of a real number and an imaginary number.