perpendicular bisectors and circles

I need help!!!!!!!

1. points a (8, 8,) and b (16,32) lie on a circle. the perpendicular bisector of ab is 3y + x = 72.

Find the centre of the circle.

2. three circles (circle a, b, c) all touching on lie on a line ac. the circles centres are collinear on the line ac.

circle a is (x+12)^2 + (y+15)^2=25 and c is (x-24)^2 + (y-12)^2 = 100.

find the equations of the middle b circle.

2.PQRS is a rhombus of side 4 units, K,L,M, AND N are the midpoints of PQ, QR, RS and SP, respectively.

SN is a representative of vector u and SM a representative of vector v.

Show that SK.SL (scalar product of the vectors) = 5u.v + 16

3.[list]

o, a, b are the centres of the three circles.

the two outer circles are congruent and each touches the small circle in the inside (circle a). circle a has the equation (x-12)^2 + (y+5)^2 = 25.

the three circles centres lie on a parabola whose axis of symmetry is the vertical line on centre of a.

(i) state the coordinates of a and find the length of oa

(ii) hence find the equation of the circle with the centre b

(iii) the equation of the parabola can be written in the form y= px(x +q). find the values of p and q.

It is really question **(iii)** im stuck at. question (1) is a(12, -5) and oa= 13, using the distance formula. number (2) the equation of circle b is (x-24)^2 + y^2 = 64.

thank you

thank you