Hello candidate,

I'm solving the Problem using the method of Replacement of Variables-

Lets Assume both intersects at (h,k), then this satisfies both lines.

k+m h=√ (a 2* m 2 +b 2)

⇒km−h=√ (a 2* b 2+ m 2)

⇒k 2 + m 2 - h 2 +2mhk=a 2 m 2 + b 2

⇒k 2 -m 2 +h 2 −2mhk=a 2 +b 2 m 2

⇒k 2 (m 2 +1)+h 2 =(1+m 2 )=a 2 (1+m 2 )+b 2 + (1+m 2 )

⇒k 2 +h 2 =a 2 +b 2

⇒x 2 +y 2 = a 2 +b 2 .

Hope you found it informational!!