What is the shortest distance from the origin to the circle defined by \(x^2-24x +y^2+10y +160=0\)?
You have to add 9 to both sides to make two perfect square binomials, then put it into the correct format of the circle equation
Thus, the center of the circle is (12,-5)
Using the pythagorean theorem, you get 12^2+5^2=169
The square root of 169 is 13, thus your answer is 13