   Chapter 10, Problem 9PS

Chapter
Section
Textbook Problem

# Area Let a and b be positive constants. Find the area of the region in the first quadrant bounded by the graph of the polar equation r = a b ( a sin θ + b cos θ ) ,   0 ≤ θ ≤ π 2 .

To determine

To calculate: The area of the region in the first quadrant bounded by the graph of the polar equation r=abasinθ+bcosθ,0θπ2

Explanation

Given:

The provided polar equation is:

r=abasinθ+bcosθ,0θπ2

Where, a,b are positive constant.

Formula used:

Area of triangle =12ab where a,b are base and height of a triangle.

Convert the polar equation into rectangular form x=rcosθ and y=rsinθ.

Calculation:

Solve the equation as below:

r=abasinθ+bcosθr(asinθ+bcosθ)=abasinθ+bcosθ×(asinθ+bcosθ)

r(asinθ+bcosθ)=ab …...…... (1)

Now, convert the polar equation into rectangular form assume x=rcosθ and y=rsinθ

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