The conic represented by x = 2(cos t + sin t) | vedclass

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(C) Given equations are $x = 2(\cos t + \sin t)$ and $y = 5(\cos t - \sin t)$.Dividing by the coefficients,we get $\frac{x}{2} = \cos t + \sin t$ and

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(C) Given equations are $x = 2(\cos t + \sin t)$ and $y = 5(\cos t - \sin t)$.Dividing by the coefficients,we get $\frac{x}{2} = \cos t + \sin t$ and $\frac{y}{5} = \cos t - \sin t$.Squaring both equations:$(\frac{x}{2})^2 = \cos^2 t + \sin^2 t + 2 \sin t \cos t = 1 + \sin(2t)$$(\frac{y}{5})^2 = \cos^2 t + \sin^2 t - 2 \sin t \cos t = 1 - \sin(2t)$Adding the two squared equations:$(\frac{x}{2})^2 + (\frac{y}{5})^2 = (1 + \sin(2t)) + (1 - \sin(2t)) = 2$$\frac{x^2}{4} + \frac{y^2}{25} = 2$Dividing by $2$:$\frac{x^2}{8} + \frac{y^2}{50} = 1$This is the standard equation of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.

The conic represented by $x = 2(\cos t + \sin t), y = 5(\cos t - \sin t)$ is .....

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