Question

equation of a circle
tracy goycochea
standard equation of a circle formula explained!
write the standard - form equation for circle j with a center at the origin and a diameter of 18.
pergunta aberta
what are the coordinates of the origin? (x,y)=(?,?)
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Explanation:

Step1: Recall circle - equation formula

The standard - form equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\). When the center is at the origin \((h = 0,k = 0)\), the equation becomes \(x^{2}+y^{2}=r^{2}\).

Step2: Calculate the radius

Given the diameter \(d = 18\), and the relationship \(r=\frac{d}{2}\), so \(r=\frac{18}{2}=9\).

Step3: Write the circle equation

Substitute \(r = 9\) into the equation \(x^{2}+y^{2}=r^{2}\), we get \(x^{2}+y^{2}=81\).

Answer:

\(x^{2}+y^{2}=81\)