Q:

If real number x and y satisfy $(x+5)^2 +(y-12)^2=14^2$ then find the minimum value of $x^2 +y^2$

Problem : 
If real number x and y satisfy $(x+5)^2 +(y-12)^2=14^2$ then find the minimum value of $x^2 +y^2$
Please suggest how to proceed on this question... I got this problem from  [1]: http://www.mathstudy.in/

A:

Notice that
$$(x+5)^2+(y-12)^2=14^{2}$$
represents a circle whose center is $(-5,12)$ and its radius is $14$.
On the other hand, $x^2+y^2$ represents the square of the distance between the origin and the point $(x,y)$.
Hence, what you want is the point on the circle which is the closest to the origin. Do you think you can get what you want?

