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14 October, 23:11

Show that the curve x = 6 cos (t), y = 5 sin (t) cos (t) has two tangents at (0, 0) and find their equations.

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  1. 15 October, 02:36
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    We can write

    cos (t) = x/6

    so

    y = 5 (±√ (1 - (x/6) ^2) * x/6

    Then

    y' = (±5/6) * (√ (1 - (x/6) ^2) + x / (2√ (1 - (x/6) ^2) * (-2 (x/6))

    The limit as x → 0 is ±5/6

    The equations of the two tangents are

    y = (5/6) x

    y = (-5/6) x
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