(1 / 2) P is a moving point on the circle x ^ 2 + y ^ 2 + 4x-6y = 0, find (1) fixed point Q (1, - 1) minimum value of PQ, (2) fixed point n (- 2,2), find PQ (1 / 2) P is a moving point on the circle x ^ 2 + y ^ 2 + 4x-6y = 0, find (1) the minimum value of fixed point Q (1, - 1) and (2) the minimum value of fixed point n (- 2,2) | Math enthusiast | Mathematical art

(1 / 2) P is a moving point on the circle x ^ 2 + y ^ 2 + 4x-6y = 0, find (1) fixed point Q (1, - 1) minimum value of PQ, (2) fixed point n (- 2,2), find PQ (1 / 2) P is a moving point on the circle x ^ 2 + y ^ 2 + 4x-6y = 0, find (1) the minimum value of fixed point Q (1, - 1) and (2) the minimum value of fixed point n (- 2,2)

Obviously, the standard equation for a circle is (x + 2) ^ 2 + (Y-3) ^ 2 = 13
The distance between Q and circle center is √ [(1 + 2) ^ 2 + (- 1-3) ^ 2] = 5
Therefore, the minimum value of PQ = two-point distance minus radius = 5 - √ 13

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