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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 =\
 2 years ago
 2 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 =\
 2 years ago
 2 years ago

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experimentXBest ResponseYou've already chosen the best response.0
dw:1333741791663:dw
 2 years ago

experimentXBest ResponseYou've already chosen the best response.0
the equation of circle would be x2+y2 = r2, let's take 0 0 as center for simplicity sake
 2 years ago

experimentXBest ResponseYou've already chosen the best response.0
now the slope of tangent at point p(x1, y1) would be = x1/y1
 2 years ago

experimentXBest ResponseYou've already chosen the best response.0
the slope of the radius passing through center and point P x1 y1 would be y1/x1 hence they are perpendicular to each other.
 2 years ago
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