Find the standard form of the equation of the circle having the following properties: Center at the origin Containing the point \( (-2,3) \) Type the standard form of the equation of this circle. \( \square \)

The standard form of the equation of a circle with its center at the origin \((0,0)\) is given by the formula \(x^2 + y^2 = r^2\), where \(r\) is the radius of the circle. To find the radius, we can use the distance formula to calculate the distance from the center to the point \((-2,3)\): \[ r = \sqrt{(-2 - 0)^2 + (3 - 0)^2} = \sqrt{4 + 9} = \sqrt{13}. \] Substituting \(r^2\) into the circle equation, we have: \[ x^2 + y^2 = 13. \] In standard form, the equation of the circle is \(x^2 + y^2 = 13\).