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Mathematics
Problem
If the straight line
x
−
α
l
=
y
−
β
m
=
z
−
γ
n
\frac{x-\alpha}{l} = \frac{y-\beta}{m} = \frac{z-\gamma}{n}
l
x
−
α
=
m
y
−
β
=
n
z
−
γ
intersect the curve
a
x
2
+
b
y
2
=
1
,
z
=
0
ax^2 + by^2 = 1, z = 0
a
x
2
+
b
y
2
=
1
,
z
=
0
, then prove that
a
(
α
n
−
γ
l
)
2
+
b
(
β
n
−
γ
m
)
2
=
n
2
a(\alpha n - \gamma l)^2 + b(\beta n - \gamma m)^2 = n^2
a
(
α
n
−
γ
l
)
2
+
b
(
β
n
−
γ
m
)
2
=
n
2
.
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