Math  /  Geometry

QuestionConvert these Cartesian equation to parametric equations in terms tt. \begin{tabular}{|l} (x7)2+(y6)2=1{x(t)=cos(t)+y(t)=sin(t)+\left(\frac{x}{7}\right)^{2}+\left(\frac{y}{6}\right)^{2}=1 \Longrightarrow\left\{\begin{array}{l}x(t)=\square \cos (t)+\square \\ y(t)\end{array}=\square \sin (t)+\square\right. \end{tabular}

Studdy Solution
Verify the parametric equations:
Substitute x(t)=7cos(t)x(t) = 7 \cos(t) and y(t)=6sin(t)y(t) = 6 \sin(t) back into the original Cartesian equation:
(7cos(t)7)2+(6sin(t)6)2=cos2(t)+sin2(t)=1\left(\frac{7 \cos(t)}{7}\right)^2 + \left(\frac{6 \sin(t)}{6}\right)^2 = \cos^2(t) + \sin^2(t) = 1
The identity cos2(t)+sin2(t)=1\cos^2(t) + \sin^2(t) = 1 is satisfied, confirming the correctness of the parametric equations.
The parametric equations are:
x(t)=7cos(t) x(t) = 7 \cos(t) y(t)=6sin(t) y(t) = 6 \sin(t)

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