Given that the equation of circle O is x ^ 2 + y ^ 2 = 9, find the locus of the middle point P of the circle passing through the chord of point a (1,2)? Given that the equation of circle O is x ^ 2 + y ^ 2 = 9, find the locus of the midpoint P of the chord of the circle passing through point a (1,2)? Thank you

Given that the equation of circle O is x ^ 2 + y ^ 2 = 9, find the locus of the middle point P of the circle passing through the chord of point a (1,2)? Given that the equation of circle O is x ^ 2 + y ^ 2 = 9, find the locus of the midpoint P of the chord of the circle passing through point a (1,2)? Thank you

If you take part in the college entrance examination, there is no hope to solve the problem in this way. The Olympic experts tell you the simple method
College entrance examination method 1:
P(x,y)
OP ⊥ ab
k(OP)*k(AB)=-1
(y/x)*(y-2)/(x-1)=-1
(x-0.5)^2+(y-1)^2=1.25
Method 2
P (x, y), chord ab
xA+xB=2x,yA+yB=2y
k(AB)=(yA-yB)/(xA-xB)=(y-2)/(x-1)
(xA)^2+(yA)^2=9.(1)
(xB)^2+(yB)^2=9.(2)
(1)-(2):
(xA+xB)*(xA-xB)+(yA+yB)*(yA-yB)=0
(xA+xB)+(yA+yB)*(yA-yB)/(xA-xB)=0
2x+2y*(y-2)/(x-1)=0
x^2-x+y^2-2y=0
(x-0.5)^2+(y-1)^2=1.25
If the Olympic master can't understand this, you have to change the liberal arts