Question: The circle C has equation x 2 4x + y 2 6y = 7. The line l with equation x 3y +

The circle C has equation x² − 4x + y² − 6y = 7. The line l with equation x − 3y + 17 = 0 intersects the circle at the points P and Q.

a. Find the coordinates of the point P and the point Q.

b. Find the equation of the tangent at the point P and the point Q.

c. Find the equation of the perpendicular bisector of the chord PQ.

d. Show that the two tangents and the perpendicular bisector intersect at a single point and find the coordinates of the point of intersection.

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