Which one of the following equations,represen | vedclass

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(B) Option $(A): x = 3 \cos t, y = 4 \sin t$Eliminating $t$,we get $\frac{x^2}{9} + \frac{y^2}{16} = 1$,which is an ellipse.Option $(B): x^2 - 2 = -2

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$x^2 - 2 = -2 \cos t; y = 4 \cos^2 \frac{t}{2}$

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(B) Option $(A): x = 3 \cos t, y = 4 \sin t$Eliminating $t$,we get $\frac{x^2}{9} + \frac{y^2}{16} = 1$,which is an ellipse.Option $(B): x^2 - 2 = -2 \cos t \Rightarrow x^2 = 2 - 2 \cos t = 2(1 - \cos t)$.Also,$y = 4 \cos^2 \frac{t}{2} = 2(1 + \cos t)$.From the first,$\cos t = 1 - \frac{x^2}{2}$.Substituting into $y$: $y = 2(1 + 1 - \frac{x^2}{2}) = 2(2 - \frac{x^2}{2}) = 4 - x^2$.This is $x^2 = -(y - 4)$,which is a parabola.Option $(C): \sqrt{x} = 	an t, \sqrt{y} = \sec t$Eliminating $t$ using $\sec^2 t - 	an^2 t = 1$,we get $y - x = 1$,which is a straight line.Option $(D): x = \sqrt{1 - \sin t}, y = \sin \frac{t}{2} + \cos \frac{t}{2}$$x^2 = 1 - \sin t$ and $y^2 = 1 + \sin t$.Adding them,$x^2 + y^2 = 2$,which is a circle.

Which one of the following equations,represented parametrically,represents a parabolic profile?

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