1. Largest Value of m?

Hi, I was told that this was a simple calculus problem so I thought I should post it here.

What is the largest value of m such that the graph of the equation y=mx meets the graph of the equation (x-10)^2 + (y-5)^2 =4

Thanks for any help.

2. $\displaystyle (x-10)^2+(y-5)^2=4$ and $\displaystyle y=mx$

$\displaystyle (x-10)^2+(mx-5)^2=4$

$\displaystyle x^2-20x+100+m^2x^2-10mx+25=4$

$\displaystyle x^2(1+m^2)-x(20+10m)+121=0$

Then use the quadratic equation to find the largest value of m.

3. Ok, I did the quadratic equation for it, but now am stumped. I have:

(-444x-464mx)/(4x^2 +4m^2 x^2) and (-484x-484mx)/(4x^2 +4m^2 x^2)

What do I do now?

4. Originally Posted by Showcase_22
$\displaystyle (x-10)^2+(y-5)^2=4$ and $\displaystyle y=mx$

$\displaystyle (x-10)^2+(mx-5)^2=4$

$\displaystyle x^2-20x+100+m^2x^2-10mx+25=4$

$\displaystyle x^2(1+m^2)-x(20+10m)+121=0$

Then use the quadratic equation to find the largest value of m.
Note that the discriminant is $\displaystyle (20 + 10m)^2 - 4(1 + m^2)(121)$.