u can post only one q at a time
i'm solvin 1st q
letz solve dis by elimination of options
substitute x=1-y in da parabola
solve da quadratic in y u have 2 get a positive soln and a negative soln if u substitute the value of a frm options.a&b cant be possible.
so 4 c u get 2 values one positive and negative
and by goemetry u can get da the 2 chords r latus rectum and a perpendicular 2 da given line
so da length of latus rectum must be 4
hope i'm right