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Mathematics
Mathematics
Problem
If the pair of straight lines
A
x
2
+
2
H
x
y
+
B
y
2
=
0
Ax^2 + 2Hxy + By^2 = 0
A
x
2
+
2
H
x
y
+
B
y
2
=
0
be conjugate diameters of 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
, then prove that
A
a
2
=
B
b
2
Aa^2 = Bb^2
A
a
2
=
B
b
2
.
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