Question

determine the equation of the circle graphed below.

Explanation:

Step1: Find the center of the circle

The center of the circle is given as \((h,k)=(2, - 3)\)

Step2: Calculate the radius

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let \((x_1,y_1)=(2,-3)\) (center) and \((x_2,y_2)=(3,2)\) (a point on the circle)

$$r=\sqrt{(3 - 2)^2+(2+ 3)^2}=\sqrt{1 + 25}=\sqrt{26}$$

Step3: Write the equation of the circle

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\). Substitute \(h = 2\), \(k=-3\) and \(r=\sqrt{26}\)

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Answer:

\((x - 2)^2+(y + 3)^2=26\)