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Chapter 6: Problem 60

Convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. $$r=10$$

Short Answer

Expert verified
The polar equation \(r = 10\) converts to the rectangular equation \(x^2 + y^2 = 100\), which represents a circle with radius 10 on the rectangular coordinate system.

Step by step solution

01

Polar to Rectangular Conversion

The conversion of polar coordinates \((r, \theta)\) to rectangular coordinates \((x, y)\) can be accomplished using the relationships \(x = r\cos(\theta)\) and \(y = r\sin(\theta)\). Here, though, our equation is simply \(r = 10\), representing points that are 10 units away from the origin, regardless of their angle. The equation \(r = 10\) can be written in rectangular coordinates as \(x^2 + y^2 = 100\). This is a circle with a radius of 10 units, centered at the origin.
02

Plot the Equation

Plot the equation \(x^2 + y^2 = 100\) on a rectangular coordinate system. This is a circle centered at the origin (0,0) with a radius of 10 units. To plot it, identify the center and draw a circle with diameter 10 units.

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