   Chapter 10.2, Problem 41E

Chapter
Section
Textbook Problem

Eliminating a Parameter In Exercises 39-42, eliminate the parameter and obtain the standard form of the rectangular equation.Ellipse: x = h + a cos θ ,   y = k + b sin θ

To determine

To calculate: The rectangular equation of an ellipse by the elimination of the parametric

equations given as x=h+acosθ,y=k+bsinθ.

Explanation

Given:

The parametric equations of the ellipse are x=h+acosθ,y=k+bsinθ.

Formula used:

The trigonometric identity sin2θ+cos2θ=1.

Calculation:

The given parameter equations are x=h+acosθ,y=k+bsinθ.

In the equation x=h+acosθ ;

x=h+acosθxh=acosθxha=cosθ …...…... (1)

Similarly, in the equation y=k+bsinθ ;

y=k+bsinθyk=bsinθykb=sinθ …...…..

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