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Mathematics
Problem
Chords of the circle
x
2
+
y
2
=
a
2
x^2 + y^2 = a^2
x
2
+
y
2
=
a
2
touch the hyperbola
x
2
/
a
2
−
y
2
/
b
2
=
1
x^2/a^2 - y^2/b^2 = 1
x
2
/
a
2
−
y
2
/
b
2
=
1
. Prove that locus of their middle point is the curve
(
x
2
+
y
2
)
2
=
a
2
x
2
−
b
2
y
2
(x^2 + y^2)^2 = a^2x^2 - b^2y^2
(
x
2
+
y
2
)
2
=
a
2
x
2
−
b
2
y
2
.
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