Science:Math Exam Resources/Courses/MATH105/April 2014/Question 03 (b)/Solution 1

We want to find where ${\sqrt {(x-(-1))^{2}+(y-2)^{2}}}$ attains its minimum on the circle $x^{2}+y^{2}=125$.

Equivalently, we need to find where $(x-(-1))^{2}+(y-2)^{2}=(x+1)^{2}+(y-2)^{2}$ is the smallest on the circle $x^{2}+y^{2}=125$. From part (a), we know that this function has its minimum on the circle 80 at the point $(-5,10).$