eliminate the parameter and indicate the direction of increasing t?

x=2cos(t)

y=5sin(t)

Could somebody do it step by step, so i could understand the process. that'd be great. Thanks

1 Answer

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  • Lisa
    Lv 5
    9 years ago
    Favorite Answer

    x = 2cos(t) ⇔ x/2 = cos(t) ⇔ x²/4 = cos²t

    y = 5sin(t) ⇔ y/5 = sin(t) ⇔ y²/25 = sin²t

    Add them together to get x²/4 + y²/25 = cos²t + sin²t = 1

    Hence the curve is an ellipse centered at the origin with the y-axis as the major axis

    Plug in various values of t = 0, π, 2π, 3π ... nπ will give you a trace of the ellipse from counterclockwise.

    Yin

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