Question: Let P(5, 12) be a point on the circle x 2 + y 2 = 169 (see figure). (a) What is the slope of the

Let P(5, −12) be a point on the circle x2 + y2 = 169 (see figure).

-6 -2 2 y 0 -6- Figure for 4 2 P(3, 4)

(a) What is the slope of the line joining P and O(0, 0)?

(b) Find an equation of the tangent line to the circle at P.

(c) Let Q(x, y) be another point on the circle in the fourth quadrant. Find the slope mx of the line joining P and Q in terms of x.

(d) Calculate lim x→5 mx. How does this number relate to your answer in part (b)?

-6 -2 2 y 0 -6- Figure for 4 2 P(3, 4) Q 6 -X

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