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

 Mar 14, 2020
 #1
avatar+486 
+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

 Mar 14, 2020
edited by SpongeBobRules24  Mar 14, 2020
 #2
avatar+22085 
+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
avatar+486 
+6

I fixed my answer, thank you for noticing.

 Mar 14, 2020
edited by SpongeBobRules24  Mar 14, 2020
 #4
avatar+22085 
+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

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