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Chapter 6: Problem 59

Convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. $$r=8$$

Short Answer

Expert verified
The equivalent Cartesian (rectangular) equation for the given polar equation \(r = 8\) is \(x^2 + y^2 = 64\), which graphs as a circle centered at the origin with a radius of 8 units.

Step by step solution

01

Convert the polar equation to a rectangular (Cartesian) equation

The given polar equation is \(r = 8\). Recall that in Cartesian coordinates, \(r^2= x^2 + y^2\). So, replace \(r\) with 8 in this equation, we get \(64 = x^2 + y^2\). This is a standard equation for a circle centered at the origin with radius 8.
02

Graph the Cartesian equation

Plot the circle on a Cartesian grid. Center it at the origin (0, 0) and draw a circle with a radius of 8 units. This graph represents the same points as the polar equation \(r = 8\).

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