Question

a circle has a radius of \\(\sqrt{98}\\) units and is centered at \\((5.9, 6.7)\\). write the equation of this circle.

Explanation:

Step1: Recall the standard equation of a circle

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

Step2: Identify the values of \(h\), \(k\), and \(r\)

Given that the center \((h,k)=(5.9,6.7)\) and \(r = \sqrt{98}\). Then \(r^{2}=(\sqrt{98})^{2}=98\).

Step3: Substitute the values into the standard equation

Substitute \(h = 5.9\), \(k = 6.7\), and \(r^{2}=98\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 5.9)^2+(y - 6.7)^2=98\).

Answer:

\((x - 5.9)^2+(y - 6.7)^2=98\)