Check the solution to "A pair of parametric equations is given. Find..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Suman Cole

Answered question

2021-08-14

A pair of parametric equations is given. Find a rectangular-coordinate equation for the curve by eliminating the parameter.

x = 2 \cos t, y = 3 \sin t, 0 \leq t \leq 2 π

Answer & Explanation

Jayden-James Duffy

Skilled2021-08-15Added 91 answers

To eliminate the parameter, we use the Pythagorean Identity $\sin^{2} θ + \cos^{2} θ = 1$ . Solving $x = 2 \cos t$ for $\cos t$ gives $\cos t = \frac{x}{2}$ . Solving $y = 3 \sin t$ for $\sin t$ gives $\sin t = \frac{y}{3}$ . Substituting these into the identity then gives:

$(\frac{y}{3})^{2} + (\frac{x}{2})^{2} = 1$

$\frac{y^{2}}{9} + \frac{x^{2}}{4} = 1$

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