+8 What is the shortest distance from the origin to the circle defined by \(x^2-24x +y^2+10y +160=0\)?
+1072 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
(x^2-24x+144)+(y^2+10y+25)=9
(x-12)^2+(y+5)^2=9
(x-12)^2+(y+5)^2=3^2
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
+37146 Pretty good SBR...BUT the question does not ask for the radius...it asks for how far from the ORIGIN (0,0) to the circle......
I would calculate the distance from the origin to the CENTER (h,k)...then subtract the radius....
+37146 Getting there.....now yo have the distance to the center of the circle......not to the circle itself.....you need to subtract the radius
