What is the equation of the tangent to the circle x^2 + y^2 = 25 at the point (3, 4)?

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The equation of the circle is x^2 + y^2 = 25. The equation of the tangent at the point (3, 4) needs to be determined.

For a function f(x), the slope of the tangent at the point where x = c is equal to f'(c).

x^2 + y^2 = 25

using implicit differentiation

=> 2x + 2y*y' = 0

=> y' = -2x/2y = -x/y

At the point (3, 4) the slope is -3/4

The equation of the tangent is (y - 4)/(x - 3) = -3/4

=> 4(y - 4) = -3(x - 3)

=> 4y - 16 = -3x + 9

=> 4y + 3x = 25

The equation of the tangent to the circle x^2 + y^2 = 25 at (3, 4) is 4y + 3x - 25 = 0

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