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Mathematics
Mathematics
Problem
Show that the line
l
x
+
m
y
+
n
=
0
lx + my + n = 0
l
x
+
m
y
+
n
=
0
will cut the ellipse
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
in points whose eccentric angles differ by
(
π
/
2
)
(\pi/2)
(
π
/2
)
, if
a
2
l
2
+
b
2
m
2
=
2
n
2
a^2l^2 + b^2m^2 = 2n^2
a
2
l
2
+
b
2
m
2
=
2
n
2
.
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