anonymous
  • anonymous
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 =\
Mathematics
schrodinger
  • schrodinger
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experimentX
  • experimentX
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experimentX
  • experimentX
the equation of circle would be x2+y2 = r2, let's take 0 0 as center for simplicity sake
experimentX
  • experimentX
now the slope of tangent at point p(x1, y1) would be = -x1/y1

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experimentX
  • experimentX
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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