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 $(-5,10).$