Application of circle and equation The chord length of line L: 2x-y-2 = 0 cut by circle C: (x-3) & sup2; + Y & sup2; = 9

Application of circle and equation The chord length of line L: 2x-y-2 = 0 cut by circle C: (x-3) & sup2; + Y & sup2; = 9

From the equation of straight line L, y = 2 (x-1) is brought into the equation of circle (x-3) & sup2; + 4 (x-1) & sup2; = 9, which is reduced to 5x & sup2; - 14x + 4 = 0
|X1-x2 | = [2 √ (144 & sup2; - 4 * 5 * 4)] / 10 = (2 √ 29) / 5 (PS: x1, X2 can be solved from the equation or written directly by formula method)
Chord length = │ x1-x2 * √ (k ^ 2 + 1) = (2 √ 29) / 5 * √ (2 & sup2; + 1) = (2 √ 145) / 5