Hi, can you please help me with this question? I have also attached the solution. I understand most of the solution, however, I don't understand how they got L=k(7,-1). Thanks :)

4. [4 marks] Let p = 1 and q = 7. Find the pole of the line ( with equation qx - py = 1 in the circle C(O, 2), (i.e. the circle centred at the origin with radius 2).If p:1andq:7 Then the point D on E that is closest to O is the intersection of E and the line with equation SE + 73/ = 0 (as that line goes through 0 and is orthogonal to 19,). So L' : (7/50, l/50). Thus pole of, is then L, the inverse of L' in the circle. But L : M7, 1) for some k, and as 0L : lam/5U and OL' : 1/\\/ 50 and CL - OL' : 4, we have k : 4 and the pole is (28, 4)