JEE Advanced 2020 Full Test 1 Paper 2

If points A,B,C,D are concyclic, then ac= bd. The coordinates of the points of intersection of lines are (‌

ac(b−d)

bc−ad

,‌

bd(c−a)

bc−ad

) Let coordinates of the point of intersection be (h,k)

Then, h=‌

ac(b−d)

bc−ad

,k=‌

bd(c−a)

bc−ad

Given, c2+a2=b2+d2. Since, ac=bd
So, (c−a)2=(b−d)2 or (c−a)=±(b−d)
Then the locus of the points of intersection is y=±x