Final answer:
To find the exact values of k for which the line is tangent to the circle, we need to set the equation of the line equal to the equation of the circle and solve for k. Substituting y = kx+3 into the equation of the circle, we get a quadratic equation in x. Solving this equation will give us the exact values of k.
Step-by-step explanation:
To find the exact values of k for which the line y = kx+3 is tangent to the circle with center (6,3) and radius 2, we need to set the equation of the line equal to the equation of the circle and solve for k. The equation of the circle is (x-6)^2 + (y-3)^2 = 4. Substituting y = kx+3 into the equation of the circle, we get (x-6)^2 + (kx+3-3)^2 = 4. Expanding and simplifying this equation, we get a quadratic equation in x. Solving this equation will give us the exact values of k.
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