The equation with the parametric equations x - 1 - cos - y - 2 - 3 sin - represents an ellipse-

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Parametric Representation: Ellipse

The equation ...

Question

The equation with the parametric equations x = 1 + cos $θ$ , y = 2 + 3 sin $θ$ represents an ellipse.

False

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True

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Solution

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θ

(2 cos θ + 3 sin θ) x + (3 cos θ - 5 sin θ) y - (5 cos θ - 2 sin θ) = 0

(2 c o s θ + 3 s i n θ) x + (3 c o s θ - 5 s i n θ) y - (5 c o s θ - 2 s i n θ) = 0

θ

θ

θ

θ

x = 1 + 4 c o s θ, y = 2 + 3

θ

x = 3 (cos t + sin t)

y = 4 (cos t - sin t)

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