What is the shortest distance from the origin to the circle defined by \(x^2-24x +y^2+10y +160=0\)?

awesauce15 Mar 14, 2020

#1**+6 **

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

SpongeBobRules24 Mar 14, 2020

#2**+1 **

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....

ElectricPavlov
Mar 14, 2020

#3

#4**+1 **

Getting there.....now yo have the distance to the center of the circle......not to the circle itself.....you need to subtract the radius

ElectricPavlov
Mar 14, 2020