If the ends of the hypotenuse of a right angled triangle are (0, a) and (a, 0) then the locus of the third vertex is

Step-by-step solution

Let A B C be a right angled triangle with the ends of hypotenuse A(0, a) and C(a, 0) Let co-ordinates of point B is B(x, y) According to Pythagorous theorem, aligned & (A C)^2=(A B)^2+(B C)^2 & aligned ( a^2+a^2 )^2= ( (x-0)^2+(y-a)^2 )^2 aligned & + ( (x-a)^2+(y-0)^2 ) & 2 a^2=x^2+(y-a)^2+(x-a)^2+y^2 & x^2+y^2-a x-a y=0 aligned