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Chapter 1: Problem 70

Write the standard form of the equation of the circle with the given characteristics. Center: \((0,0) ;\) Radius: 5

Short Answer

Expert verified
The standard form equation of the circle is \(x^2 + y^2 = 25\).

Step by step solution

01

Identify the given circle

The center of the circle is at the origin \( (0,0) \) and the radius of the circle is 5.
02

Standard form of the circle

The standard form of a circle equation is \( (x-h)^2 + (y-k)^2 = r^2 \), where \( (h,k) \) is the center and \( r \) is the radius of the circle.
03

Substitute the values into the equation

Substitute the given values into the equation, \(h = 0\), \(k = 0\), and \(r = 5\). Hence, the standard form of the equation becomes \( (x-0)^2 + (y-0)^2 = 5^2 \). This simplifies further to \( x^2 + y^2 = 25 \).

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