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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Chapter
Section
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

  1. (a) Eliminate the parameter to find a Cartesian equation of the curve.
  2. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

12. x = 1 2 cos θ , y = 2 sin θ, 0 ≤ θπ

(a)

To determine

To find: obtain a Cartesian equation of the curve by eliminating parameter t .

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=12cosθ

2x=cosθ (1)

The parametric equation for the variable y is as follows.

y=2sinθ

12y=sinθ (2)

The range of t is 0 to π .

Calculation:

Square and add both the Equations (1) and (2)

(2x2)2+(12y)2=cos2θ+sin2θ

Put 1 for cos2θ+sin2θ in the above equation.

(4x2)+(14y2)=1x2(12)2+y222=1

The Cartesian equation of the curve is x2(12)2+y222=1

(b)

To determine

To plot: The curve using the parametric equations. x=12cosθ and y=2sinθ .

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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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