If x a + y b =1 and x c + y d =1 where a, b, c, d>0 intersect the axes at four con-cyclic points and a^2+c^2=b^2+d^2 , then the lines can intersect at which of the following given points?

Step-by-step solution

aligned & a c=b d [power of point] & a^2+c^2=b^2+d^2 aligned (a-c)^2=(b-d)^2 and (a+c)^2=(b+d)^2 a+c=b+d and a-c=b-d aligned & a=b and c=d & Both line have slope =-1 Parallel lines never meet aligned aligned & a-c=a-b & a=d and b=c aligned x d + y c =1 ; x c + y d =1 aligned & c x+d y=d x+c y c(x-y)=d(x-y) & y=x & 2 lines meet y=x . aligned