Question

(e) When newspapers were printed by lithograph, the newsprint had to run over three rollers, illustrated in the diagram below by three circles. The centres A, B and C of the three circles are collinear. The equations of the outer circles are (x + 12)2 + (y+15)2 = 25 and (x−24)2 +(y−12)2 = 100. Find the equation of the central circle.

Figure 1:

[10 Marks] i. Show that the equation of the tangent at the point P = (x1,y1) of the circle

2 2 ?x1 +g? x+y+2gx+2fy+c=0isgivenbyy−y1=− y1+f (x−x1).

[9 Marks]

ii. Show that the vector equation of a line is given by r = r0 + tv where

r, r0 ∈ V (V ector space) and t a parameter. [8 marks]

Answer 1