What is the shortest distance from the origin to the equation #x^2-18+y^2-20y+172=0#?

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Answer 1 · 2016-10-08T10:17:07

#10.4536#

To have a real solution, I will assume that the equation is

#x^2-18x+y^2-20y+172=0#

This is a circle such as

#(x-x_0)^2+(y-y_0)^2= r^2# with

#-2x_0 = -18->x_0 = 9#
#-2y_0=-20->y_0=10#
#x_0^2+y_0^2-r^2=172->r=3#

so the distance from the origin is

#norm(O-p_0)-r = sqrt(x_0^2+y_0^2)-r =sqrt(181)-3 =10.4536 #