The line y = mx + 1 intersects the circle x 2 + y 2 19x

Question:

The line y = mx + 1 intersects the circle x2 + y2 − 19x − 51 = 0 at the point P(5, 11).

a. Find the coordinates of the point Q where the line meets the curve again.

b. Find the equation of the perpendicular bisector of the line PQ.

c. Find the x-coordinates of the points where this perpendicular bisector intersects the circle.

Give your answers in exact form.

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