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 x^2 + y^2 = r^2 - (BLANK)+2yy' = 0 - y'= (BLANK) , so the slope of the tangent line at (x0, y0) is (BLANK). The negative reciprocal of that slope is (BLANK), which is the slope of OP, so the tangent line at P is perpendicular to the radius OP.

PLEASE HELP!!

Question

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 x^2 + y^2 = r^2 -> (BLANK)+2yy' = 0 -> y'= (BLANK) , so the slope of the tangent line at (x0, y0) is (BLANK). The negative reciprocal of that slope is (BLANK), which is the slope of OP, so the tangent line at P is perpendicular to the radius OP.

PLEASE HELP!!

isaiah.feynman · Answer

First differentiate the circle's equation implicitly!

isaiah.feynman · Answer

Then find y'

anonymous · Answer

hold on I put 2xx' because it looks like 2yy' is that not right?

anonymous · Answer

it told me I was wrong with that already

anonymous · Answer

please help me I do not know how to do this. I know I need to differentiate but how!

anonymous · Answer

this is really frustrating thank you for telling me what I already know.

isaiah.feynman · Answer

attachment

anonymous · Answer

but on my webassign it says it equals zero.

isaiah.feynman · Answer

Oh yes. The radius is constant so it should be zero.

anonymous · Answer

ok thank you

isaiah.feynman · Answer

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