EXAMPLE 1 dy (a) If x2 + y? = 400, find Y. dx (b) Find an equation of the tangent to the circle x + y² = 400 at the point (12, 16). SOLUTION 1 (a) Differentiating both sides of the equation x²+y = 400: (400) dx +. = 0. xp Remembering that y is a function of x and using the Chain Rule, we have dy dx !! dx Thus 2x + = 0. dx Now we solve this equation for dy/dx: dx (b) At the point (12, 16) we have x = 12 and y = 16, so dy dx An equation of the tangent to the circle at (12, 16) is therefore (x - %3D or

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