Question

determine the equation of the circle with center (3,0) containing the point (-2,√56).

Explanation:

Step1: Find the radius

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(3,0)\) and \((x_2,y_2)=(-2,\sqrt{56})\).

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Step2: Write the equation of the 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 and \(r\) is the radius. Here, \(h = 3\), \(k = 0\) and \(r = 9\).

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Answer:

\((x - 3)^2+y^2=81\)