The curve represented by x = 3(cos t + sin t) | vedclass

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(A) Given equations are $x = 3(\cos t + \sin t)$ and $y = 4(\cos t - \sin t)$.Dividing by the coefficients,we get $\frac{x}{3} = \cos t + \sin t$ and

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Ellipse

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(A) Given equations are $x = 3(\cos t + \sin t)$ and $y = 4(\cos t - \sin t)$.Dividing by the coefficients,we get $\frac{x}{3} = \cos t + \sin t$ and $\frac{y}{4} = \cos t - \sin t$.Squaring both equations:$(\frac{x}{3})^2 = \cos^2 t + \sin^2 t + 2 \sin t \cos t = 1 + \sin 2t$$(\frac{y}{4})^2 = \cos^2 t + \sin^2 t - 2 \sin t \cos t = 1 - \sin 2t$Adding the two squared equations:$\frac{x^2}{9} + \frac{y^2}{16} = (1 + \sin 2t) + (1 - \sin 2t) = 2$Dividing by $2$,we get $\frac{x^2}{18} + \frac{y^2}{32} = 1$.This is the equation of an ellipse.

The curve represented by $x = 3(\cos t + \sin t)$ and $y = 4(\cos t - \sin t)$ is

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