For what values of k does the line y=kx-1 have two distinct points of intersection with the circle (x-2)^2+(y-3)^2=2?

sub y=kx-1 into circle equation, get (k^2+1)x^2-(8k+4)x+18=0for 2 distinct solutions need b^2-4ac>0, ie -8k^2+64k-56>0iff k^2-8k+7<0complete the square: intersections of equation in k satisfy(k-4)^2=9 so inequality satisfied when 1<k<7. strict inequality for distinct intersection