   Chapter 10.2, Problem 40E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The rectangular equation of a circle by the elimination of the parametric equations given as x=h+rcosθ,y=k+rsinθ.

Explanation

Given:

The given parametric equations of the circle is x=h+rcosθ,y=k+rsinθ.

Formula used:

The trigonometric identity sin2θ+cos2θ=1.

Calculation:

The parameter equations are x=h+rcosθ,y=k+rsinθ.

In the equation, x=h+rcosθ

x=h+rcosθxh=rcosθxhr=cosθ …...…... (1)

Similarly, in the equation y=k+rsinθ:

y=k+rsinθyk=rsinθykr=sinθ

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