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Mathematics
Problem
Prove that the line
l
x
+
m
y
−
n
=
0
lx + my - n = 0
l
x
+
m
y
−
n
=
0
will be a normal to the hyperbola
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
if
a
2
l
2
−
b
2
m
2
=
(
a
2
+
b
2
)
2
n
2
.
\frac{a^2}{l^2} - \frac{b^2}{m^2} = \frac{(a^2 + b^2)^2}{n^2}.
l
2
a
2
−
m
2
b
2
=
n
2
(
a
2
+
b
2
)
2
.
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