If (1+ax)n=1+8x+24x2+.... and a line through (a,n)  cuts the circle x2+y2=4  in A and B, then PA.PB=

Given (1+ax)n=1+8x+24x2+..... ⇒1+n1!ax+n(n−1)2!a2x2+.....=1+8x+24x2+......Equating the coefficients of x  and x2 , we getna=8                                                                                                                  … (i)n(n−1)2a2=24                                                                                             … (ii)From (i), n2a2=64                                                                                        … (iii)Dividing (ii) by (iii), we get n−12n=38⇒4n−4=3n  ⇒n=4From (i), a=2Given circle is x2+y2−4=0                                                                    … (iv)Let P≡(a,n) , then P≡(2,4)Now, PA.PB=PC2=22+42−4=16