Parametrization of Implicitly Defined Functions
AP Precalculus · Flashcards · Recall
AP PRECALCULUS · FLASHCARDS
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QUESTION
Parametrize the hyperbola
x
2
−
y
2
=
1
x^2 - y^2 = 1
x
2
−
y
2
=
1
.
QUESTION
What is the parametric form for the hyperbola
x
2
−
y
2
=
a
2
x^2 - y^2 = a^2
x
2
−
y
2
=
a
2
?
QUESTION
Identify the parametric form of the ellipse
x
2
+
4
y
2
=
4
x^2 + 4y^2 = 4
x
2
+
4
y
2
=
4
.
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ANSWER
x
=
2
cos
(
t
)
,
y
=
sin
(
t
)
x = 2\text{cos}(t), y = \text{sin}(t)
x
=
2
cos
(
t
)
,
y
=
sin
(
t
)
. Ellipse in form
x
2
4
+
y
2
=
1
\frac{x^2}{4} + y^2 = 1
4
x
2
+
y
2
=
1
uses appropriate scaling.
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