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Chapter 1: Problem 69

Write the standard form of the equation of the circle with the given characteristics. Center: \((0,0) ;\) Radius: 4

Short Answer

Expert verified
The standard form of the equation of the circle with center at \((0,0)\) and radius 4 is \( x^2+y^2=16 \).

Step by step solution

01

Understand the standard form of a circle's equation

The standard form of a circle's equation is \( (x-a)^2 + (y-b)^2 = r^2 \), where \( (a, b) \) represents the coordinates of the center and \( r \) is the radius.
02

Substituting the values

Given that the circle's center is at \((0,0)\) and its radius is 4, substitute these values into the equation. This gives \( (x-0)^2 + (y-0)^2 = 4^2 \)
03

Simplifying the equation

Simplifying \((x-0)^2\) and \((y-0)^2\) yields \(x^2\) and \(y^2\) respectively. Similarly, \(4^2\) can be simplified to 16. Therefore, the standard form of the circle's equation is \( x^2+y^2=16 \).

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Most popular questions from this chapter

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(P\) varies directly as \(x\) and inversely as the square of \(y .\) \(\left(P=\frac{28}{3} \text { when } x=42 \text { and } y=9 .\right)\)

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