amaths_circle

1(a)
The equation of PA
(y-y0)/(x-x0)=(y1-y0)/(x1-x0)
(x-x0)(y1-y0)=(x1-x0)(y-y0)
xy1-x0y1-xy0=x1y-x0y-x1y0
(y1-y0)x+(x0-x1)y+(x1y0-x0y1)=0
Since
OA^2+PA^2=PO^2
r^2+(x0-x1)^2+(y0-y1)^2=x0^2+y0^2
We have x0x1+y0y1=r^2
(b)
Similarly we have x0x2+y0y2=r^2
Since the equation of x0x+y0y=r^2 suitable for A,B
We prove that x0x+y0y=r^2 represents a straight line passing through A and B
(c)
The equation of AB
4x-y=9