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Mathematics
Mathematics
Problem
Show that the line
x
cos
α
+
y
sin
α
=
p
x \cos \alpha + y \sin \alpha = p
x
cos
α
+
y
sin
α
=
p
touches the hyperbola
x
2
a
2
−
y
2
b
2
=
1
if
a
2
cos
2
α
−
b
2
sin
2
α
=
p
2
.
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \quad \text{if} \quad a^2 \cos^2 \alpha - b^2 \sin^2 \alpha = p^2.
a
2
x
2
−
b
2
y
2
=
1
if
a
2
cos
2
α
−
b
2
sin
2
α
=
p
2
.
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