The trajectory equation () of the midpoint of each chord passing through a point P (1,1) in the circle (X-2) ^ 2 + (Y-2) ^ 2 = 4? (x-3 / 2) ^ 2 + (Y-3 / 2) ^ 2 = 1 / 2 (in known circle)

The trajectory equation () of the midpoint of each chord passing through a point P (1,1) in the circle (X-2) ^ 2 + (Y-2) ^ 2 = 4? (x-3 / 2) ^ 2 + (Y-3 / 2) ^ 2 = 1 / 2 (in known circle)

Let the midpoint Q (m, n) be connected to the center t,
Then TQ bisects the chord vertically
So TQ Λ 2 + QP Λ 2 = Pt Λ 2
(m-2)∧2+(n-2)∧2+(m-1)∧2+(n-1)∧2=(2-1)∧2+(2-1)∧2
Finishing: m ∧ 2-3m + n ∧ 2-3n + 4 = 0
(m-3/2)∧2+(n-3/2)∧2-9/2+4=0
So the trajectory equation of the midpoint is: (x-3 / 2) ^ 2 + (Y-3 / 2) ^ 2 = 1 / 2

Elden Ring Premiere

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