# Given #x^2 + (y – 2)^2 = 4 # how do you derive a parametric equation?

The parametric equations are

We use the following parametric equations

Therefore,

So,

The parametric equations are

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To derive a parametric equation from the equation (x^2 + (y - 2)^2 = 4), you can let (x = r \cos(\theta)) and (y = r \sin(\theta)), where (r) represents the radius and (\theta) represents the angle.

Substitute these expressions for (x) and (y) into the given equation and solve for (r): [ (r \cos(\theta))^2 + ((r \sin(\theta)) - 2)^2 = 4 ]

Simplify the equation and solve for (r).

Once you have found (r) as a function of (\theta), you can write the parametric equations: [ x = r \cos(\theta) ] [ y = r \sin(\theta) ]

where (r) is the expression you found earlier in terms of (\theta). This will give you the parametric equations representing the curve defined by the equation (x^2 + (y - 2)^2 = 4).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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