hiiiiiiiiiii
the first question....
its a bit tym-taking to typ all the aolution...so here's the method
let any line y-mx+c intersect the curve at two distinct points, then homogenise the equation of curve with given line's equation, nd then equating the sum of coeffecients of xsqr and y sqr, u'll get a relation in m and c, which will show that line passes thru a fixed pint...nd that fixed point comes out to be (1,2)
any problem while solving ask again!!!