Please explain the position relationship between line and circle in senior one, thank you! (17 11:15:35) Given circle C: x2 + y2-4x-14y + 45 = 0 and point Q (- 2,3) If P (m, M + 1) is on circle C, find the length of line PQ and the slope of line PQ; If P is any point on the circle C, find the maximum and minimum of PQ length If the real numbers a and B satisfy A2 + b2-4a-14b + 45 = 0, find the value range of k = (B-3) / (a + 2)

Please explain the position relationship between line and circle in senior one, thank you! (17 11:15:35) Given circle C: x2 + y2-4x-14y + 45 = 0 and point Q (- 2,3) If P (m, M + 1) is on circle C, find the length of line PQ and the slope of line PQ; If P is any point on the circle C, find the maximum and minimum of PQ length If the real numbers a and B satisfy A2 + b2-4a-14b + 45 = 0, find the value range of k = (B-3) / (a + 2)

1. The equation is: (X-2) ^ 2 + (Y-7) ^ 2 = 8, P (m, M + 1) on circle C, (m-2) ^ 2 + (M + 1-7) ^ 2 = 8, M = 4, M + 1 = 5, P (4,5). According to the two-point distance formula, | PQ | = √ [(4 + 2) ^ 2 + (5-3) ^ 2] = 2 √ 10, PQ slope: k = (5-3) / (4 + 2) = 1 / 3.2, | PQ | maximum value should be connected to the center of the circle, and the diameter should be away from