Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If the line
y
=
m
x
+
a
2
m
2
−
b
2
y = mx + \sqrt{a^2 m^2 - b^2}
y
=
m
x
+
a
2
m
2
−
b
2
touches 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
at the point
(
a
sec
θ
,
b
tan
θ
)
(a \sec \theta, b \tan \theta)
(
a
sec
θ
,
b
tan
θ
)
, show that
θ
=
sin
−
1
(
b
a
m
)
\theta = \sin^{-1} \left( \frac{b}{am} \right)
θ
=
sin
−
1
(
am
b
)
.
Browse the problem library