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calyne

  • 4 years ago

Show, using implicit differentiation, that any tangent line at a point P to a circle with center O is perpendicular to the radius OP. I can visualize it/draw a diagram but the actual calculations aren't quite clear to me still =\

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  1. experimentX
    • 4 years ago
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    |dw:1333741791663:dw|

  2. experimentX
    • 4 years ago
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    the equation of circle would be x2+y2 = r2, let's take 0 0 as center for simplicity sake

  3. experimentX
    • 4 years ago
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    now the slope of tangent at point p(x1, y1) would be = -x1/y1

  4. experimentX
    • 4 years ago
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    the slope of the radius passing through center and point P x1 y1 would be y1/x1 hence they are perpendicular to each other.

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