Let from the point with abscissa 25, two tangents are drawn to the ellipse 24x2+25y2=600  with foci at S1 and S2. The points of contact of tangents are A and B. If the distance of A fromS1 is  6013 units, then

x225+y224=1,a=5,b=26,e=15So the point is on the directrix x=ae=25So, AB is a focal chord, also as 1SA+1SB=2ab2If S1A=6015 then S1B=5Also S1A+S2A=2a=10=S1B+S2BS2A=10-S1A=7013,S2B=10-S1B=5,      Distance from the directrix =1e×distance from the focus 7013×5=35013,