Answers and Explanations 277
Answers
401–500
422.
y = 1
You know a point on the tangent line, so you just need to find the slope. Begin by
simplifying the left side of the equation.
y y
x
y
y
y
x
y
2
2
2
4
2
2
1
− =
−
=
(
) tan
tan
Next, find the derivative:
4
2
2
2
3
2
y
dy
dx
y
dy
dx
x
y x
y
dy
dx
−
=
+
(tan )
sec






Use the values x = 0 and y = 1 and solve for the slope
dy
dx
:
4 1
2 1
0
2
0
0
3
( )
( )
dy
dx
dy
dx
dy
dx
dy
dx
−
=
=
=
The tangent line has a slope of 0 and passes through (0, 1), so its equation is
y
x
y
− =
−
1 0
0
1
(
)
=