Questions: Find the standard form of the equation of the circle having the following properties: Center at the origin Containing the point (6,-9) Type the standard form of the equation of this circle.

Solution Steps

To find the radius of the circle, we use the distance formula between the center of the circle at the origin \((0, 0)\) and the given point \((6, -9)\):

\[ r = \sqrt{(6 - 0)^2 + (-9 - 0)^2} = \sqrt{6^2 + (-9)^2} = \sqrt{36 + 81} = \sqrt{117} \approx 10.8167 \]

The standard form of the equation of a circle with center at the origin \((0, 0)\) and radius \(r\) is given by:

\[ x^2 + y^2 = r^2 \]

Substituting \(r = 10.8167\):

\[ r^2 = (10.8167)^2 \approx 117.0 \]

Thus, the equation of the circle is:

\[ x^2 + y^2 = 117.0 \]

Final Answer