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

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Advance Math

15. Let r be a positive real number. The equation for a circleof 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 0and b does not equal 0. Determine the slope of the line tangent tothe circle at the point (a,b).

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

Hint: Two lines (neither of which is horizontal) areperpendicular if and only if the products of their slopes is equalto

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