15. Let r be a positive real number. The equation for a circle of radius r...

15. Let r be a positive real number. The equation for a circle of radius r whose center is the origin is (x^2)+(y^2)= r^2 .

(a) Use implicit differentiation to determine dy/dx .

(b) Let (a,b) be a point on the circle with a does not equal 0 and b does not equal 0. Determine the slope of the line tangent to the circle at the point (a,b).

(c) Prove that the radius of the circle to the point (a,b) is perpendicular to the line tangent to the circle at the point (a,b).

Hint: Two lines (neither of which is horizontal) are perpendicular if and only if the products of their slopes is equal to

Expert Solution

Colby Messinger answered 2 years ago

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