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16 February, 21:25

R=8cos (theta) - 10sin (theta) to cartesian coordinates

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  1. 16 February, 21:36
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    Convert polar equation (R, Ф):

    (1) R = 8cos Ф - 10sin Ф into Cartesian (x, y)

    We know that:

    x = R. cos Ф → cos Ф = x/R, and

    y = R. sin Ф → sin Ф = y/R

    and that x² + y² = R²

    Replace in

    R = 8cos Ф - 10sin Ф, cos Ф and sin Ф by the related x and y:

    R = 8 (x/R) - 10 (y/R)

    Multiply both sides by R:

    R² = 8R (x/R) - 10R (y/r) ↔ R² = 8x - 10y, but we have also R² = x² + y². hence: 8x - 10y = x² + y²

    OR x² + y² - 8x + 10y = 0

    We can continue in completing th squares of (x² - 8x + ?) and (y² + 10y + ?)

    (x² - 8x + ?) = (x - 4) ² - 16

    and (y² + 10y + ?) = (y + 5) ² - 25

    Final Equation:

    (x - 4) ² - 16 + (y + 5) ² - 25 →→→ (x - 4) ² + (y + 5) ² = 41
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