# Polynomial word problems

Find all points on the circle $x^2 + y^2 = 9$ that are 3.5 units from $(4,5)$

and

Find the point on the circle $x^2 + y^2 = 9$ that is closest to $(4,5)$.

I only need to set both x and y to a common variable -- then I can use a graphing calculator to find the results.

• Why "polynomial word"? The title doesn't make sense to me... – draks ... Dec 14 '13 at 21:51

For the first problem solve these 2 equations: $$x^2 + y^2 = 9$$ $$(x-4)^2 + (y-5)^2 = 3.5^2$$
For the second problem solve these 2 equations: $$x^2 + y^2 = 9$$ $$4y=5x$$