急!F5 Equations of Circles 8q14

(a) Since angle OAM = angle OBM = 90 degree. So OMAB is a cyclic quadrilateral ( angle in the same segment equal).
(ii) So angle POB = angle AMP = 45 degree ( angle in the same segment).
(bi) MB is the vertical line passing through B ( - 4, 0), so line MB is x = - 4
or x + 4 = 0
(bii)
Since angle POB = 45 degree and angle PBO is a rt. angle, so PB = OB = 4
so P is ( - 4, 4) = center of circle.
PB = radius of circle = 4
so equation of circle is
(x + 4)^2 + (y - 4)^2 = 4^2 = 16