Mathematics, 09.07.2020 05:01 zariasimone2
Show, using implicit differentiation, that any tangent line at a point P to a circle with center O is perpendicular to the radius OP. If the circle has radius r, its equation is x2 + y2 = r2 β + 2yy' = 0 β y' = , so the slope of the tangent line at P(x0, y0) is . The negative reciprocal of that slope is , which is the slope of OP, so the tangent line at P is perpendicular to the radius OP.
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Show, using implicit differentiation, that any tangent line at a point P to a circle with center O i...
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