Application of Calculus to Analytic Geomtry Problem

Hello everyone,

I have two questions on which I would greatly appreciate help. I have also included the given solution below.

**Problem:**

http://img193.imageshack.us/img193/2...ithdiagram.png

**Question #1: **For part (iii), is it possible to solve it using calculus?

By Implicit Differentiation, the circle has "slope": .

The required line has slope and the equation:

The line is tangent to the circle when .

Substitution of the equation of the line at the point of tangency gives:

.

But this does not appear to help too much.

**Question #2: This question is based on part (v), but I am trying to find something else that is not asked by the question.**

Since , the vertex of the triangle is inside the circle.

This means that we are in the case where .

The question does not ask for this, but how would I show that

By basic algebra:

but .

Thank you very much for your help.

**Given solution:**

http://img833.imageshack.us/img833/9359/solutionf.png

Re: Application of Calculus to Analytic Geomtry Problem

Have you considered common denominators?

vs.

or

vs.

so

vs.

Or, since everyone is positive

vs.

Re: Application of Calculus to Analytic Geomtry Problem

Thanks TKHunny, for answering Question #2. I should have thought of that!

May I ask if that has been any insight into **Question #1**?

Re: Application of Calculus to Analytic Geomtry Problem

I'm a little puzzled why you would want to think of another solution.

The obvious geometry is so glaring.