Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
If
(
x
−
a
)
cos
θ
+
y
sin
θ
=
a
(x - a) \cos \theta + y \sin \theta = a
(
x
−
a
)
cos
θ
+
y
sin
θ
=
a
and
tan
(
θ
2
)
−
tan
(
ϕ
2
)
=
2
b
\tan\left(\frac{\theta}{2}\right) - \tan\left(\frac{\phi}{2}\right) = 2b
tan
(
2
θ
)
−
tan
(
2
ϕ
)
=
2
b
, then a.
y
2
=
2
a
x
−
(
1
−
b
2
)
x
2
y^2 = 2ax - (1 - b^2)x^2
y
2
=
2
a
x
−
(
1
−
b
2
)
x
2
b.
tan
θ
2
=
1
x
(
y
+
b
x
)
\tan \frac{\theta}{2} = \frac{1}{x}(y + bx)
tan
2
θ
=
x
1
(
y
+
b
x
)
c.
y
2
=
2
b
x
−
(
1
−
a
2
)
x
2
y^2 = 2bx - (1 - a^2)x^2
y
2
=
2
b
x
−
(
1
−
a
2
)
x
2
d.
tan
ϕ
2
=
1
x
(
y
−
b
x
)
\tan \frac{\phi}{2} = \frac{1}{x}(y - bx)
tan
2
ϕ
=
x
1
(
y
−
b
x
)
Browse the problem library