locus

8
(a)
the equation of the circle
(x-p/2)^2+y^2=p^2/4
AB=BO
B is the mid-point of AO
so the x-coordinate of B is p/4
sub into the equation of the circle
(p/4-p/2)^2+y^2=p^2/4
p^2/16+y^2=p^2/4
y^2=(3/16)p^2
y=(√3/4)p
the coordinates of B in terms of p
=(p/4, (√3/4)p)
(b)
the coordinate of A in terms of p
=(p/2, (√3/2)p)
tan ㄥAOC=AC/OC

tan ㄥAOC=[(√3/2)p]/(p/2)
tan ㄥAOC=√3
ㄥAOC=60
(c)
the coordinate of A in terms of p

=(p/2, (√3/2)p)