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The question is (in parametric equations):

$x = 2\sin(t)$ $y = \cos(t)$

for $0 \le t \le \pi/2$

I need to eliminate the parameter and the sketch the curve... any ideas?

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    Do you know an ellipse?2012-08-28

1 Answers 1

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Hint: The parametric equation (almost) looks like that of a circle and in particular we have $\frac{x^2}{2^2} + y^2 = 1$ Do you know what kind of curve this describes? How much of the curve is traversed? In what direction?

For further reference, see here.

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    No! That would give you$a$degree four curve, namely $x^2 + y^2 - rx^2y^2 = 0.$ An ellipse is a conic section, so has a degree two equation: $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. All of the $a$, $b$, $c$, $f$, $g$ and $h$ are fixed numbers of your choice. If h^2 - ab < 0 then you have an ellipse, if $h^2-ab = 0$ then you have a parabola. If h^2 - ab > 0 then you have a hyperbola.2012-08-28