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(a) Find parametric equations for the ellipse $ x^2/a^2 + y^2/b^2 = 1 $. [Hint: Modify the equations of the circle in Example 2.](b) Use these parametric equations to graph the ellipse when $ a = 3 $ and $ b = 1 $, $ 2 $, $ 4 $, and $ 8 $.(c) How does the shape of the ellipse change as $ b $ varies?

(a) $x=a \cos t, \quad y=b \sin t, \quad 0 \leq t \leq 2 \pi$(b) See Graph(c) As $b$ increases, the ellipse stretches vertically.

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Campbell University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:18

(a) Find parametric equati…

01:56

Parametric Equations for C…

03:02

$31-36=$ Parametric Equati…

02:20

Solids of revolution Consi…

00:46

Find parametric equations …

02:56

An equation of an ellipse …

03:42

04:26

Graphing Shifted Ellipses …

03:59

04:02

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In mathematics, integration is one of the two main operations in calculus, w…

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Use Formula 11 to find the curvature.

$ y = xe^x $

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Use the binomial series to expand the function as a power series. State the …

03:35

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the giv…

02:42

A stone is dropped from the upper observation deck (the Space Deck) of the C…

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Find the length of the curve.

$ r(t) = \sqrt{2} t i + e^t j + e^{-t …

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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