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Mathematics
Problem
Prove that the locus of mid-points of the portion of the tangents to the ellipse
x
2
a
2
+
y
2
b
2
=
1
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
a
2
x
2
+
b
2
y
2
=
1
intercepted between the axes is
a
2
y
2
+
b
2
x
2
=
4
x
2
y
2
a^2 y^2 + b^2 x^2 = 4x^2 y^2
a
2
y
2
+
b
2
x
2
=
4
x
2
y
2
.
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