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Mathematics
Mathematics
Problem
If the normal at any point
P
P
P
of 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
, meets the major and minor axes in
G
G
G
and
H
H
H
respectively and
C
C
C
in the centre of the ellipse, then prove that
a
2
(
C
G
)
2
+
b
2
(
C
H
)
2
=
(
a
2
−
b
2
)
2
a^2(CG)^2 + b^2(CH)^2 = (a^2 - b^2)^2
a
2
(
C
G
)
2
+
b
2
(
C
H
)
2
=
(
a
2
−
b
2
)
2
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