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Chapter 9: Q. 10 (page 630)

x2+y2-8x+4y-5=0the variables r and u represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x, y). (b) Identify the equation and graph it.

r2+4rsin胃-8rcos胃=5

Short Answer

Expert verified

Polar equation as an equation in rectangular coordinates is x2+y2-8x+4y-5=0

Step by step solution

01

Step 1. Given data

r2+4rsinu-8rcosu=5

02

Step 2. Substitute the values of sinθ and cosθ and simplify the equation

we know,

sin胃=yx2+y2and cos胃=xx2+y2

Substituting in the given equation,

x2+y2+4(x2+y2)yx2+y2-8(x2+y2)xx2+y2=5

Above equation can be simplified as,x2+y2-8x+4y-5=0

03

Step 3. Plotting the graph

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Most popular questions from this chapter

Identify and graph each polar equation. Verify your graph using a graphing utility.
r=2+4cos胃

In Problems 11-22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.

-2+3i.

In Problems55鈥�66, the rectangular coordinates of a point are given. Find polar coordinates for each point.

3,0

Write the expression in the standard form a+bi.

3cos5蟺18+isin5蟺186

Identify and graph each polar equation. Verify your graph using a graphing utility

r=3-3sin胃
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