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Mathematics
Mathematics
Problem
PQ is the chord joining the points
ϕ
1
\phi_1
ϕ
1
and
ϕ
2
\phi_2
ϕ
2
on 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
ϕ
1
−
ϕ
2
=
2
α
\phi_1 - \phi_2 = 2\alpha
ϕ
1
−
ϕ
2
=
2
α
, where
α
\alpha
α
is constant, prove that PQ touches the hyperbola
x
2
a
2
cos
2
α
−
y
2
b
2
=
1.
\frac{x^2}{a^2} \cos^2 \alpha - \frac{y^2}{b^2} = 1.
a
2
x
2
cos
2
α
−
b
2
y
2
=
1.
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