Question

find the locus of the vertex of a right angled triangle the ends of whose hyptenuse [4,0] and [0,4]

Answer 1

Let P(x, y) be a point on locus.
From the information provided,
$(x-4)x+y(y-4)=0$
$x^{2}+y^{2}-4x-4y=0$.
Locus represents "Circle" with Centre: (2, 2); Radius: 2√2.

Answer 2

Let Q(x, y) be a point on locus.
according to question
(x-4)x + y(y-4) = 0
xsquare+ ysquare -4x-4y = 0
Locus represents "Circle" with Centre: (2, 2); Radius: 2√2.