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Mathematics
Mathematics
Problem
A circle of constant radius
r
r
r
passes through the origin
O
O
O
, and cuts the axes at
A
A
A
and
B
B
B
. Show that the locus of the foot of the perpendicular from
O
O
O
to
A
B
AB
A
B
is
(
x
2
+
y
2
)
2
(
x
−
2
+
y
−
2
)
=
4
r
2
(x^2 + y^2)^2 (x^{-2} + y^{-2}) = 4r^2
(
x
2
+
y
2
)
2
(
x
−
2
+
y
−
2
)
=
4
r
2
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